Let G be a nonabelian group of order 253=23(11), let P<G be a Sylow 23-subgroup and...

Let G be a nonabelian group of order 253=23(11), let P<G be a Sylow 23-subgroup and Q<G a Sylow 11-subgroup.

a. What are the orders of P and Q. (Explain and include any theorems used).

b. How many distinct conjugates of P and Q are there in G? n23? n11? (Explain, include any theorems used).

c. Prove that G is isomorphic to the semidirect product of P and Q.

Expert Solution

Colby Messinger answered 2 years ago

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