Recent content by basukinjal

ok. Sorry for that, here are my attempts. 1. Since (ab)^p = a^p.b^p, i tried to construct a homomorphism phi, such that phi(x) = x^p. Then the kernel for this would not be just e since p | o(G) thus, this is not a isomorphism.. and i got stuck there after. 2. 432= 2^4*3^3. So i tried to...

1. Let G be a fintie group whose order is divisible by a prime p. Assume that (ab)^p = a^p.b^p for all a,b in G. Show that the p-Sylow subgruop of G is normal in G. 2. Find the number of Abelian groups of order 432. 3. Let G be a group of order 36 with a subgroup H of order 9. Show that H...

If H is a subgroup of G then N(H) is defined as { x belonging to G | xHx^-1 = H }. If P is p-Sylow subgroup of G, then prove that N(N(P)) = N(P).