Explore: Multiply Transitive Groups

Mathieu (1861, 1873). They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objects. They are the first sporadic groups to be discovered. Sometimes

groups and are all almost simple groups. Multiply transitive group Dixon, John D.; Mortimer, Brian (1996), Permutation groups, Graduate Texts in Mathematics

finite symmetric group whose action is 2-transitive) and more generally multiply transitive groups is well-studied in finite group theory. An action

Cheng, Yuanyou (1986). "A generalization of Burnside's lemma to multiply transitive groups". Journal of Hubei University of Technology. ISSN 1003-4684..

permutation groups was revived in the 1950s by H. Wielandt whose German lecture notes were reprinted as Finite Permutation Groups in 1964. 2-transitive group Rank

Robert L. (1998), Twelve sporadic groups, Springer, p. 5, ISBN 978-3-540-62778-4 Isaacs, I. Martin (2008), Finite group theory, AMS, p. 245, ISBN 978-0-8218-4344-4

theory) Jordan's theorem (multiply transitive groups) (group theory) Krull–Schmidt theorem (group theory) Kurosh subgroup theorem (group theory) L-balance theorem

symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their

gives all finite simple groups, together with their order, the size of the Schur multiplier, the size of the outer automorphism group, usually some small

sporadic groups and was introduced by Mathieu (1861, 1873). It is a 4-fold transitive permutation group on 23 objects. The Schur multiplier and the outer