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A Cayley graph for the free product of the cyclic groups C3 and C5 (with the natural generating set). Drawn in TikZ :)

In group theory, a cyclic number is a positive integer such that every group with that number of elements must be cyclic. Learn more at expii.

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Proof: Let G = (a) be a cyclic group generated by a. Its trivial subgroup {e} containing the identity in of G, is cyclic. Let H be any nontrivial subgroup G.