Explore: Infinite Automorphism Groups

mathematics, the outer automorphism group of a group, G, is the quotient, Aut(G) / Inn(G), where Aut(G) is the automorphism group of G and Inn(G) is the

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

group, the automorphism group of G . {\displaystyle G.} For all abelian groups there is at least the automorphism that replaces the group elements by

of An; further orthogonal groups 2Dn, from the order 2 automorphism of Dn; the new series 2E6, from the order 2 automorphism of E6; the new series 3D4

ασ of the group X(F) Any automorphism π of the Dynkin diagram induces an automorphism απ of the group X(F). The Steinberg and Chevalley groups can be constructed

an outer automorphism induced by transposing conjugate elements in F4 (the field automorphism). PGL(3,4) can therefore be extended to the group PΓL(3,4)

can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced

automorphism group of the graph consisting of a path infinite to both sides. Correspondingly, it is the isometry group of Z (see also symmetry groups

the surface X admits infinitely many conformal automorphisms (in fact, the conformal automorphism group is a complex Lie group of dimension three for

finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic