Please work on part a), part b) and part c)!! Thank you very much!!
(This question needs to use Sylow theorem!)
(Groups of order G p2q). Let G p q where p and q are distinct odd primes a) Suppose p q and q t p 1. rove that G is abelian and write down the possible groups. Find three combinations of primes p, that satisfy these conditions and one pair that does not. b) Suppose q p and p t q 1. Prove that G is abelian. Find three combinations of primes that satisfy the conditions and one that does not. c) Construct a non-abelian group of order G 72 3 using semi-direct products
Show transcribed image text(Groups of order G p2q). Let G p q where p and q are distinct odd primes a) Suppose p q and q t p 1. rove that G is abelian and write down the possible groups. Find three combinations of primes p, that satisfy these conditions and one pair that does not. b) Suppose q p and p t q 1. Prove that G is abelian. Find three combinations of primes that satisfy the conditions and one that does not. c) Construct a non-abelian group of order G 72 3 using semi-direct products
