Assume(adsbygoogle = window.adsbygoogle || []).push({}); Gis a finite group and [tex]H = \left\{ {g \in G|g^n = e} \right\}[/tex] for any [tex]n>0[/tex].eis identity.

I have been able to show that ifGis cyclic, thenHhas at mostnelements.

However, I can't go the other way. That is, assumingHhas at mostnelements, I haven't been able to say anything about whetherGis cyclic, abelian or neither.

Any suggestions?

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# Properties of finite groups

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