(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose a finite group has exactly n elements of order p where p is prime. Prove that either n=0 or p divides n + 1.

2. Relevant equations

My professor says that this proof is similiar to the proof of Lagrange's Theorem, in our Abstract Algebra book (Gallian).

3. The attempt at a solution

I am so lost with this question. It is a "special problem" we've been given to work on all semester. I have tried letting H represent a subgroup of the finite group, and using the elements of order p in the original group to form left cosets of H in the group. Not sure I really understand that. Not sure where that is getting me. I am not used to feeling so lost when tackling a problem.

Please...can anyone steer me in the right direction?

Thank you!

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# Homework Help: Proof similiar to Lagrange's?

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