Given a Group G, can we choose any non-identity element and say that this element will be the generator of a cyclic group contained in G ?
2026-03-26 02:51:27.1774493487
Can any element of a group generate a cyclic group?
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No only we can say it as furthermore it is indeed true. If $g\in G$, $\langle g\rangle$ is always a cyclic group (and a subgroup of $G$, of course).