I think that the this group contains the 5 element cycles and the identity e but overall I'm not sure how to prove that the product of the 2 members of H is also a 5 cycle or e.
2026-04-01 11:39:42.1775043582
If $G = S_5$ and $H = \{g \in G \mid g^{5} = e\}$ how could I determine and prove whether or not $H$ is a subgroup of $G$?
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Note that $$(1\,2\,3\,4\,5)(1\,2\,3\,5\,4)=(1\,3)(2\,4)$$