Thread: AutoMorphism

Let g be a finite group and let f in Aut(G) with all g in G, f(g)=g iff g=e
Show that all g in G, there exist a in G s.t. g=a^(-1).f(a)

Originally Posted by mathemanyak

Let g be a finite group and let f in Aut(G) with all g in G, f(g)=g iff g=e
Show that all g in G, there exist a in G s.t. g=a^(-1).f(a)

let and suppose that for some then and thus i.e.

thus


think about this: do we really need to be an automorphism or being homomorphism is enough?