Reference no: EM131416957

Recall that an automorphism of a group G is a group isomorphism from G to G. Denote the set of all automorphism of G by Aut(G)

a) Show that Aut(G) is also a group

b) Recall that for each g belongs to G, the map c: G--G defined by c(x)=gxg^(-1) is an element of Aut(G). Show that the map c: g---c is a homomorphism from G to Aut(G)

c) Show that the kernel of the map c is Z(G)

d) In general, the map c is not surjective. The image of c is called the group of inner automorphisms and denoted Int(G). Conclude that Int(G) = G/Z(G)