Abstract Algebra: Theory and Applications · Problem 11.5.1

Matrix Groups and Symmetry — Thomas Judson

Mathematics — Abstract Algebra · automorphism-group

Problem

Let

\text{Aut}(G)

be the set of all automorphisms of

G

; that is, isomorphisms from

G

to itself. Prove this set forms a group and is a subgroup of the group of permutations of

G

; that is,

\text{Aut}(G) \leq S_G