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Let G be a finite non-abelian simple group and let p be a prime. We classify all pairs (G,p) such that the sum of the complex irreducible character degrees of G is greater than the index of a Sylow p-subgroup of G. Our classification includes all groups of Lie type in defining characteristic p (because every Gelfand-Graev character of G is multiplicity free and has degree equal to the above index), and a handful of well-described examples.

For most (and possibly all) non-associative finite simple Moufang loops, three generators of order 3 can be chosen so that each two of them generate a group isomorphic to $(3, 3 | 3, p)$. The subgroup structure of $(3, 3 | 3, p)$ depends on the solvability of a certain quadratic congruence, and it is described here in terms of generators.

We prove that if $G$ is a finite simple group of Lie type and $S$ a subset of $G$ of size at least two then $G$ is a product of at most $c\log|G|/\log|S|$ conjugates of $S$, where $c$ depends only on the Lie rank of $G$. This confirms a conjecture of Liebeck, Nikolov and Shalev in the case of families of simple groups of Lie type of bounded rank.

We determine upper bounds for the maximum order of an element of a finite almost simple group with socle T in terms of the minimum index m(T) of a maximal subgroup of T: for T not an alternating group we prove that, with finitely many exceptions, the maximum element order is at most m(T). Moreover, apart from an explicit list of groups, the bound can be reduced to m(T)/4. These results are applied to determine all primitive permutation groups on a set of size n that contain permutations of order greater than or equal to n/4.

In this paper we find the number of conjugate $\pi$-Hall subgroups in all finite almost simple groups. We also complete the classification of $\pi$-Hall subgroups in finite simple groups and correct some mistakes from our previous paper.

In this paper we find the number of conjugate $\pi$-Hall subgroups in all finite almost simple groups. We also complete the classification of $\pi$-Hall subgroups in finite simple groups and correct some mistakes from our previous paper.

In this paper we find the number of conjugate $\pi$-Hall subgroups in all finite almost simple groups. We also complete the classification of $\pi$-Hall subgroups in finite simple groups and correct some mistakes from our previous paper.

In this report we summarize this work, all finite simple groups $G$ can determined uniformly using their orders $|G|$ and the set $\pi_e(G)$ of their element orders.

Assume that a finite almost simple group with simple socle isomorphic to an exceptional group of Lie type possesses a solvable Hall subgroup. Then there exist four conjugates of the subgroup such that their intersection is trivial.

Finite groups are said to be isospectral if they have the same sets of element orders. A finite nonabelian simple group $L$ is said to be almost recognizable by spectrum if every finite group isospectral to $L$ is an almost simple group with socle isomorphic to $L$. It is known that all finite simple sporadic, alternating and exceptional groups of Lie type, except $J_2$, $A_6$, $A_{10}$ and $^3D_4(2)$, are almost recognizable by spectrum. The present paper is the final step in the proof of the following conjecture due to V.D. Mazurov: there exists a positive integer $d_0$ such that every finite simple classical group of dimension larger than $d_0$ is almost recognizable by spectrum. Namely, we prove that a nonabelian composition factor of a~finite group isospectral to a finite simple symplectic or orthogonal group $L$ of dimension at least 10, is either isomorphic to $L$ or not a group of Lie type in the same characteristic as $L$, and combining this result with earlier work, we deduce that Mazurov's conjecture holds with $d_0=60$.

Here we study the automorphism groups of $1$-designs constructed from finite nonabelian simple groups by using two methods presented in Moori (Information Security, Coding Theory and Related Combinatorics, 2011). We obtain some general results for both and improve one of these methods. In an application to the sporadic Mathieu groups $M_{n}$, we are able to retrieve the Steiner systems $S(t,t+3,n)$ where $(n,t)\in\{(22,3),(23,4),(24,5)\}$.

In noncommutative geometry a `Lie algebra' or bidirectional bicovariant differential calculus on a finite group is provided by a choice of an ad-stable generating subset C stable under inversion. We study the associated Killing form. For the universal calculus associated to C=G \ {e} we show that the magnitude of the Killing form \mu=\sum_{a,b\in C}K^{-1}_{a,b} is defined for all finite groups (even when K is not invertible) and that a finite group is Roth, meaning its conjugation representation contains every irreducible, iff \mu\ is not equal to 1/(N-1), where N is the number of conjugacy classes. We show further that the Killing form is invertible in the Roth case, and that the Killing form restricted to the (N-1)-dimensional subspace of invariant vectors is invertible iff the finite group is almost-Roth group (meaning its conjugation representation has at most one missing irreducible). It is known that most finite simple groups are Roth and that all are almost Roth. At the other extreme from the universal calculus we prove that the generating conjugacy class in the case of the dihedral groups D_{2n} with n odd has invertible Killing form, and the same for the 2-cycles conjugacy class in any S_n. We also compute some eigenvalues of the Killing form in the case of the n-cycles class in S_n. Finally, we verify invertibility of the Killing forms of all real conjugacy classes in all nonabelian finite simple groups to order 75,000, by computer, and we conjecture this to extend to all nonabelian finite simple groups.

Let $H_k(W,q)$ be the Iwahori--Hecke algebra associated with a finite Weyl group $W$, where $k$ is a field and $0 \neq q \in k$. Assume that the characteristic of $k$ is not ``bad'' for $W$ and let $e$ be the smallest $i \geq 2$ such that $1+q+q^2+... +q^{i-1}=0$. We show that the number of simple $H_k(H,q)$-modules is ``generic'', i.e., it only depends on $e$. The proof uses some computations in the {\sf CHEVIE} package of {\sf GAP} and known results due to Dipper--James, Ariki--Mathas, Rouquier and the author.

The subgroup of the Schur multiplier of a finite group G consisting of all cohomology classes whose restriction to any abelian subgroup of G is zero is called the Bogomolov multiplier of G. We prove that if G is quasisimple or almost simple, its Bogomolov multiplier is trivial.

Let $F_g$ denote the closed orientable surface of genus $g$. What is the least order finite group, $G_g$, for which there is a homomorphism $\psi$ from $\pi_1(F_g)$ to $G_g$ so that no nontrivial simple closed curve on $F_g$ represents an element in Ker($\psi$)? For the torus it is easily seen that $G_1 = Z_2 \times Z_2$ suffices. We prove here that $G_2$ is a group of order 32 and that an upper bound for the order of $G_g$ is given by $g^{2g +1}$. The previously known upper bound was greater than $2^{g{2^{2g}}}$.

In representation theory of finite groups an important role is played by irreducible characters of p-defect 0, for a prime p dividing the group order. These are exactly those vanishing at the p-singular elements. In this paper we generalize this notion investigating the irreducible characters that are constant at the p-singular elements. We determine all such characters of non-zero defect for alternating, symmetric and sporadic simple groups. We also classify the irreducible characters of quasi-simple groups of Lie type that are constant on the non-identity unipotent elements. In particular, we show that for groups of BN-pair rank greater than 2 the Steinberg and the trivial characters are the only characters in question. Additionally, we determine all irreducible characters whose degrees differ by 1 from the degree of the Steinberg character.

In representation theory of finite groups an important role is played by irreducible characters of p-defect 0, for a prime p dividing the group order. These are exactly those vanishing at the p-singular elements. In this paper we generalize this notion investigating the irreducible characters that are constant at the p-singular elements. We determine all such characters of non-zero defect for alternating, symmetric and sporadic simple groups. We also classify the irreducible characters of quasi-simple groups of Lie type that are constant on the non-identity unipotent elements. In particular, we show that for groups of BN-pair rank greater than 2 the Steinberg and the trivial characters are the only characters in question. Additionally, we determine all irreducible characters whose degrees differ by 1 from the degree of the Steinberg character.

A supercharacter theory for a finite group $G$ is a set of superclasses each of which is a union of conjugacy classes together with a set of sums of irreducible characters called supercharacters that together satisfy certain compatibility conditions.The aim of this paper is to give a description of some finite simple groups with exactly three or four supercharacter theories.

We prove that the groups $\text{SL}(3,\mathbb{R})$ and $\text{Sp}(2,\mathbb{R})$ do not have the $p\,$-approximation property for any $1

For a finite group generated by involutions, the involution width is defined to be the minimal $k\in\mathbb{N}$ such that any group element can be written as a product of at most $k$ involutions. We show that the involution width of every non-abelian finite simple group is at most $4$. This result is sharp, as there are families with involution width precisely 4.

We prove that the length of the shortest identity in a finite simple group of Lie type of rank $r$ defined over $\mathbb{F}_q$, is bounded (from above and below) by explicit polynomials in $q$ and $r$.

We prove that the length of the shortest identity in a finite simple group of Lie type of rank $r$ defined over $\mathbb{F}_q$, is bounded (from above and below) by explicit polynomials in $q$ and $r$.

Given a group G denote with exp(G) its exponent, which is the least common multiple of the order of its elements. In this paper we solve the problem of finding the finite simple groups having a proper subgroup with the same exponent. For each G with this property we will give an explicit example of H

Given a group G denote with exp(G) its exponent, which is the least common multiple of the order of its elements. In this paper we solve the problem of finding the finite simple groups having a proper subgroup with the same exponent. For each G with this property we will give an explicit example of H

1Merton of the Movies

By Harry Leon Wilson

<em>Merton of the Movies</em> is a comedy that centers around Merton Gill, an aspiring dramatic artist from Simsbury, Illinois who makes his way to Hollywood to become a serious actor. How could Merton fail in attaining his dreams after finishing a correspondence course from the General Film Production Company of Stebbinsville, Arkansas, certifying him to be a competent screen actor?<br><br>Harry Leon Wilson, the author, was a very popular humor writer in the first decades of the 20th century. This book was made into film several times, the last in 1947 starring Red Skelton. (Summary written by Margaret.)

2Our Nig, or, Sketches from the Life of a Free Black, In A Two-Story White House

By Harriet E. Wilson

Frado is a colored girl, living in the USA a few years before the Civil War. She is abandoned by her own white mother in the house of the Bellmont's- where she is treated badly. This is a sad book, but Frado's cheerfulness and dignity will make you love her until the end. (Introduction by Stav Nisser)

3Shakespeare and Music

By Christopher Wilson

Shakespeare's plays are full of music: love songs, comic ditties, serious ballads, and songs for witches and spirits. Over the centuries musicians and composers have also created musical adaptations based on Shakespeare's plays. Composer Christopher Wilson's Shakespeare and Music (1922) documents the musical history of each play across various genres, including opera and incidental music. (Summary by Elizabeth Klett)

4South African Memories

By Lady Sarah Wilson

Lady Sarah Isabella Augusta Wilson was the aunt of Winston Spencer Churchill. In 1899 she became the first woman war correspondent when she was recruited to cover the Siege of Mafeking for the Daily Mail during the Boer War. She moved to Mafeking with her husband at the start of the war, where he was aide-de-camp to Colonel Robert Baden-Powell. Baden-Powell asked her to leave Mafeking for her own safety after the Boers threatened to storm the British garrison. This she duly did, and set off on a madcap adventure in the company of her maid, travelling through the South African countryside until she was finally captured by the enemy and returned to the town in exchange for a horse thief being held there. Dwindling food supplies became a constant theme in the stories she sent back to the Mail and the situation seemed hopeless when the garrison was hit by an outbreak of malarial typhoid. In this weakened state the Boers managed to penetrate the outskirts of the town but the British stood firm and repelled the assault. (Summary by Wikipedia)

5And Then the Town Took Off

By Richard Wilson

The town of Superior, Ohio, certainly was living up to its name! In what was undoubtedly the most spectacular feat of the century, it simply picked itself up one night and rose two full miles above Earth! Radio messages stated simply that Superior had seceded from Earth. But Don Cort, stranded on that rising town, was beginning to suspect that nothing was simple about Superior except its citizens. Calmly they accepted their rise in the world as being due to one of their local townspeople, a crackpot professor. But after a couple of weeks of floating around, it began to be obvious that the professor had no idea how to get them down. So then it was up to Cort: either find a way to anchor Superior, or spend the rest of his days on the smallest—and the nuttiest—planet in the galaxy! (Summary From The Book)

A weary survivor of the Great War, Major Rane Smith wanders in a great ennui amidst the mystical beauties of the fjords of Norway after the War, seeking a spiritual renewal. Deep in the forest he stumbles fatefully upon the strange, almost elvish home of Karl Ingman, an iconoclastic old Ibsen scholar. There Major Smith meets Ingman's two beautiful young daughters and his eldritch wife Rosa, entering into long days of profound dialogue with each member of the family. A rare and exquisite gem of a novel, The Death of Society is one of the most remarkable books of the post-War era, showing Wilson's deep intellectual, artistic, and philosophical passions against the backdrop of a romantic passion just as profound. Fallen into a strange obscurity after her untimely death, Romer Wilson deserves a revival of reputation that was recognized in her lifetime when she was awarded the prestigious Hawthornden Prize for this novel. - Summary by Expatriate

Another remarkable World War I novel by Romer Wilson, "If All These Young Men" is a character study of a group of young 20-something friends in England dealing with the looming, grey presence of the War in their lives. The story begins on Good Friday 1918, and centers on Josephine Miller, a restless, strong-minded young woman who cannot tolerate trivialities or frivolities so long as the War goes on, and who agonizes over how to go on living in its shadow. The characters of Josephine and her friends are patterned on those of Wilson and her own coterie at the time, both male and female, revealing the profound angst of young intellectuals of the time who lived under the dread not only of invasion and national destruction, but also of the alien world that would be left for them when the monstrous conflict was over. - Summary by Expatriate

Romer Wilson's first novel is a study in the life of Genius, a theme that would preoccupy her throughout her life. The eponymous Martin Schüler is a young German composer of genius in the years leading up to the Great War. His great passion is to create one magnificent work that will live forever. With his passions so consumed in his art, he makes sacrifices in his human relationships, going through a series of wrenching, unequal love affairs. The novel is of interest not only for Schüler's lifelong struggle to reconcile his fleshly desires with his lust for fame, but also for the Continental setting as Europe falls toward catastrophe. - Summary by Expatriate

9New Freedom

By Thomas Woodrow Wilson

The book is not a discussion of measures or of programs. It is an attempt to express the new spirit of our politics and to set forth, in large terms which may stick in the imagination, what it is that must be done if we are to restore our politics to their full spiritual vigor again, and our national life, whether in trade, in industry, or in what concerns us only as families and individuals, to its purity, its self-respect, and its pristine strength and freedom. (From the Preface) - Summary by Woodrow Wilson

10Russian Storybook

By Richard Wilson

Reverend Richard Wilson went to the heart of Russia to find stories from the eastern outposts of Christianity, untouched by the renaissance or reformation. He found the nature of the stories quite different from those of more western cultures. His hope was to teach English children about their Russian counterparts in a way they would understand, so he retold the stories rather than sought translations. - Summary by Lynne Thompson

Richard Wilson has taken tales from the two great Indian epics, the Rāmāyaṇa and the Mahābhārata, as well as other early sources, and has retold them in English, in an effort to showcase to young English-speaking readers that 'oriental' stories share the same elements as tales they are used to. Love, hate, virtue, oppression, tenderness, bravery and resourcefulness and an ultimate desire to conquer evil. - Summary by Paraphrased from the Introduction

12Bunker Bean

By Harry Leon Wilson

Young, self conscious, timid stenographer for a New York businessman with a beautiful daughter (the flapper). He emulates stronger types, but alas.....is not them. He grows up in this humorous volume from 1913. - Summary by joseph tabler

LibriVox volunteers bring you 23 recordings of It Is in Winter That We Dream of Spring by Robert Burns Wilson. This was the Weekly Poetry project for March 10, 2019. <br> ------<br> Robert Burns Wilson was an American painter and poet. Although his most famous poem was based on the battle cry "Remember the Maine," he was best known during his day as a nature poet. (Summary by Wikipedia)

14Ruggles of Red Gap

By Harry Leon Wilson

A stuffy class-conscious gentleman's valet is transplanted to the rough uncivilized American northwest, where the rubes and social climbers are duly impressed with his manners and style. Will the American freedom rub off on the Englishman, or will the churlish Americans acquire some high-class polish? Witty social commentary a la P.G. Wodehouse's Jeeves and Wooster. - Summary by Carol Pelster

15Anecdotes of Big Cats and Other Beasts

By David Alec Wilson

Although David Alec Wilson is best known for his writings about Thomas Carlyle, he was a Scottish civil servant who spent much time in India. This collection of stories draw from those experiences, where tales of tigers, leopards, crocodiles, elephants and monkeys are part of the cultural fabric. These range from short vignettes to several multi-part stories, all sure to entertain. - Summary by Larry Wilson

Dr. Andrew Wilson FRSE was a Scottish physiologist and zoologist and lecturer in zoology and comparative anatomy at the University of Edinburgh and the Royal College of Surgeons of Edinburgh in the late 19th and early 20th century. In the preface of this book, he writes: "...the chief aim of the work is to present in a popular and readily understood form, the chief evidences of the evolution of living beings. In this view, whilst I have been content to assume the reality of that process, I have also endeavoured to marshal the more prominent facts of zoology and botany, which serve to prove that evolution, broadly considered is not merely a name for an unknown tendency in nature, but is an actual factor in the work of moulding the life with which the universe teems." - Summary by J. M. Smallheer

17State of the Union Addresses by United States Presidents (1913 - 1922)

By Warren G. Harding and Thomas Woodrow Wilson

The State of the Union address is a speech presented by the President of the United States to a joint session of the United States Congress, typically delivered annually. The address not only reports on the condition of the nation but also allows the President to outline his legislative agenda (for which he needs the cooperation of Congress) and national priorities. This album contains recordings of addresses from Woodrow Wilson and Warren Harding. - Summary by Wikipedia

18Able McLaughlins

By Margaret Wilson

The Able McLaughlins won the Pulitzer Prize for a novel in 1924 in Margaret Wilson's debut work. Aptly described as "Little House on the Prairie - but for adults" the novel follows a group of Scottish families who pioneer the Iowa prairie in the 1860’s. The main storyline concerns Wully, the eldest McLaughlin son, who returns home from the Civil War to find that his sweetheart, Chirstie, has experienced an unspeakable tragedy that will profoundly affect the couple's lives. Their story is one of shame and honor, secrets and guilt, fear and loathing, revenge and forgiveness. But perhaps the stars of the novel are the strong older women such as Wully’s mother, Isobel, whose love and matriarchal strength keeps the family together as well as Chirstie’s stepmother, Barbara, who finds ways to make her good-for-nothing husband keep his promises. Interlaced with the plots are richly detailed descriptions of frontier prairie life, the love that families share, and the relationships within the Scottish immigrant community. (Warren Kati)

19Wolves of God and Other Fey Stories

By Algernon Blackwood and Wilfred Wilson

Renowned author of weird fiction Algernon Blackwood, in collaboration with unknown author Wilfred Wilson, brings us a magical, sinster and ethereal collection of stories of pagan sacrifice, reincarnation, beastly vengeance and other bizarre scenarios that one often comes across when waltzing through the macabre. - Summary by Ben Tucker

20Literature of Arabia

By Epiphanius Wilson

A collection of many romantic stories: it has no epic unity. It will remind the reader of the "Morte d'Arthur" of Sir Thomas Malory, rather than of the "Iliad." The author chose the most striking of these episodes as best calculated to serve as genuine specimens of Arabian literature. They will transport the modern reader into a new world—which is yet the old, long vanished world of pastoral simplicity and warlike enthusiasm, in primitive Arabia. - Summary by Epiphanius Wilson

What Robert Dick Wilson then believed, and now believes with all his heart is this: that textual and historical Biblical controversies should be taken out of the region of subjective personal opinion, into the region of objective, clearly attested fact. It was to this task that he set himself, and no labor was to be too long or too tedious or exacting to enable him to reach that goal. - Summary by Philip E. Howard

Published between 1833 and 1841, the 90 Tracts were written by various members of "The Oxford Movement". They cover various aspects of Anglo-Catholic doctrine and other theological matters. The lead was taken by John Henry Newman (who made the largest contribution), but several other churchmen associated with Oxford University were also involved, among them John Keble, Hurrell Froude, and Edward Pusey. Among the newly written tracts were also re-prints of works from previous generations. The Tracts are of various lengths, ranging from a few pages to book-length works. The format and cheap prices, meant that the Tracts were widely disseminated. Volumes 1 and 2 also had new translations of the works of the early Fathers of the church appended to the end.<br><br> Volume 1 contains Tracts 1 to 46, along with 18 "Records of the Church". These last include all the extant epistles of St. Ignatius, alongside works by Justin Martyr, Irenæus, Clement of Alexandria, and Tertullian. Four accounts of martyrdoms and a tale of St. John round out the collection. (Summary by Beeswaxcandle)

23Old Master and Other Political Essays

By Thomas Woodrow Wilson

This is a collection of five essays published by Woodrow Wilson in 1893, while he was Professor of Jurisprudence at Princeton University (still known at the time of publication as The College of New Jersey). They had originally appeared in The New Princeton Review and The Atlantic Monthly. The essays included are The Old Master, The Study of Politics, Political Sovereignty, Character of Democracy in the United States, and Government Under the Constitution. - Summary by Ciufi Galeazzi

24Wrong Twin

By Harry Leon Wilson

With their father Dave, a classic rolling stone, out on the road, twins Merle and Wilbur lead a haphazard life. But at least they have each other. That is, until the Whipples, the richest family in town, decide to adopt one of the boys. - Summary by Mark Leder

In terms of population, in terms of development and in terms of wealth, Victoria boomed in the 1850s and 1860s due to the Gold Rush. Undeniably, the colony had money to burn. Surprise port visits by the Russian corvette Bogatyr and the Confederate warship Shenandoah in the 1860s awakened in Victoria a deep sense of vulnerability, and Victorians set their minds to a new domestic project – a decades long pursuit of security. That effort would ultimately give rise to extensive coastal fortifications, militia and artillery formations both voluntary and professional, sea mines, and a small but not inconsequential naval flotilla whose backbone would be the formidable ironclad H.M.V.S. Cerberus. Not that these efforts were confined to Victoria alone. The not-infrequently perilous straits of the Mother Country as it navigated the treacherous shoals of European politics and global empire provided ample reasons for insomnia. To varying degrees the other states too had constituted forces, and most made a start at acquiring ‘warships’—an assemblage tending more to the ‘dinky’ side than that term might otherwise suggest. But where naval matters were concerned New South Wales made something of a false start, while Queensland and South Australia simply started late. Whether this is because the issue didn’t resonate as much in the other colonies, or whether Victoria simply had larger resources to sink into an inherently (economically) unproductive project is not immediately obvious. Efforts _were_ made in all the colonies, however and joint defence and a federal fleet would be a not insignificant impetus towards Federation. The Australian colonies would largely abandon armaments acquisition with the depression of the 1890s, but the arrival of Theodore Roosevelt’s Great White Fleet in 1908 exercised popular imagination, and the recently federated Commonwealth of Australia set about acquiring a new navy. This new Royal Australian Navy, lead by the battle-cruiser HMAS Australia, steamed into Sydney Harbour for the first time in late 1913. This new institution would be tested far more strenuously than the naval forces of the unfederated colonies ever were. My appreciation to the [url=” https://www.cerberus.com.au/index.html]”Friends of the Cerberus[/url] for their extensive online resources. - Summary by Alister