Let p be a prime number such that p^k divides the order of the finite group G. Prove that the number...

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Let p be a prime number such that p^k divides the order of the finite group G. Prove that the number of subgroups of order p^k in G is congruent to 1 mod p.

David · Accepted Answer

Write   as a positive exponent and please explain your steps and why you used such steps
Given that p is a prime number such that p^k divides the order of the finite group G.

Let p be a prime number such that p^k divides the order of the finite group G. Prove that the number of subgroups of order p^k in G is congruent to 1 mod p.

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