Prasant36

Okay. Thank you Sir.

Actually both. I can prove it by using axioms & definitions, 1st by showing that H is a sgp & then its normal. But the question holds only 2 marks. So I think there is a shorter way of doing it as well. I want help regarding that. Thank you.

Let G be a group in which, (ab)^2 = (a^2)(b^2) for all a,b ∈G . Show that H = { g^2|g ∈G } is a normal subgroup of G.