Abstract Algebra: Theory and Applications · Problem 9.4.41

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · inner-automorphisms

Problem

Let

G

be a group and

g \in G

. Define a map

i_g : G \to G

i_g(x) = gxg^{-1}

. Prove that

i_g

defines an automorphism of

G

. Such an automorphism is called an inner automorphism. The set of all inner automorphisms is denoted by

\text{Inn}(G)