Question about abstract algebra.Please give detailed answer

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Oct 19th, 2015

Thank you for the opportunity to help you with your question!

Since 15 divides the order of the cyclic group G, there is exactly one subgroup H of order 15. (For example H could be Z15.) Each of the elements in H has an order which divides 15, so each element satisfies X^15 = e. So there are 15 elements in G such that  X^15 = e.

Similarly there are 20 solutions for X^20 = e.

In general, when n divides the order of a cyclic group, the number of solutions of X^n = e is n.


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Oct 19th, 2015

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