If $G$ is a finite group and $H$ and $K$ are two cyclic subgroups of same order in G . Then intersection of $H$ and $K$ is $\{e\}$ or $H=K$ . Is it true? If yes then why ?
2026-04-03 17:03:29.1775235809
Cyclic subgroups of same order
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Consider the direct product of a group of order 2 and two groups of order 3. It has several cyclic subgroups of order six and one element of order 2, which is contained in all of them.