Let n,k be positive integers and let G be a group which has k cyclic subgroups of order n. Determine with proof the number of elements of order n in G.

For example, a finite group G which has 28 cyclic subgroups of order 4 has 56 elements of order 4.

Thanks so much for taking your time!

  • 1
    $\begingroup$ You mean $k\varphi(n)$? $\endgroup$ – Alex Youcis Aug 11 '13 at 4:39
  • $\begingroup$ @Sean, did you really grasp the proof given the hint of Alex Youcis and his correct answer? $\endgroup$ – Nicky Hekster Aug 16 '13 at 19:40

Hint: In any cyclic subgroup of order $n$, there are $\varphi(n)$ generators.

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