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Counting Principle: Permutation Groups

Modern Algebra
Group Theory (CVIII)
Permutation Groups
Another Counting Principle

Using the theorem ' If O(G) = p^n , where p is a prime number, then Z(G) ≠ (e) ' as a tool, prove that
if O(G) = p^n where p is a prime number, then G has a subgroup of order p^&#945; for all 0 < &#945; &#8804; n .

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Solution Summary

This is a group theory proof regarding permutations and counting.

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