Let G be a group so that |G|=p^2q^n, for p, q primes with q > p >=3. Show that G is not simple. Hint: Look at the q-Sylow subgroups. There cannot be p of them so what happens if there are P2 of them?© BrainMass Inc. brainmass.com March 21, 2019, 7:49 pm ad1c9bdddf
We consider the Sylow q-subgroup of G with |G| = p^2 * q^n.
By the Sylow theorem, assume the number of Sylow q-subgroup is k, then we ...
Sylow Theorem is contextualized.