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# 6. (15 pts) Assume p and q are primes with p q and that G is group of order pq: Use the Sylow theorems to prove that G has a normal subgroup of order q. Prove that ...

## Question

###### 6. (15 pts) Assume p and q are primes with p q and that G is group of order pq: Use the Sylow theorems to prove that G has a normal subgroup of order q. Prove that if q # 1 mod p, then G also has a normal subgroup O1' order p. Prove that the intersection of a Sylow p-group and Sylow q-group must have order 1_

6. (15 pts) Assume p and q are primes with p q and that G is group of order pq: Use the Sylow theorems to prove that G has a normal subgroup of order q. Prove that if q # 1 mod p, then G also has a normal subgroup O1' order p. Prove that the intersection of a Sylow p-group and Sylow q-group must have order 1_  #### Similar Solved Questions

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