Let G be an abelian group of order 10. Let S={g in G | g^(-1) = g }

Then what is the number of non identity element sis S?

I think the anwer is 0.

Because We cn observe that S is a normal subgroup of G.

I define a map f : G -> G given by

f(g) = g^2 for all g in G

This is an onto homomorphism with kernel S.

So G/S ~ G

So o(G)/o(S) = o(G)

So S has just one element 'e'

Am i right.

just have one doubt. Is the homomorphism srjective??