Hi,

i was wondering if anyone could guide me through this question:

a) Suppose G is an abelian group, and let f:G->G be defined by f(x)=x^3

i) show that f is an isomorphism if |G| is not divisible by 3.

b) give an example to show that f:x->x^3 need not be a homomorphism if G is non-abelian.

c) suppose that G is a group in which x^2=e for all x in G. Prove that G is abelian.

Thanks!