- #1
Zaare
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Assume G is a finite group and [tex]H = \left\{ {g \in G|g^n = e} \right\}[/tex] for any [tex]n>0[/tex]. e is identity.
I have been able to show that if G is cyclic, then H has at most n elements.
However, I can't go the other way. That is, assuming H has at most n elements, I haven't been able to say anything about whether G is cyclic, abelian or neither.
Any suggestions?
I have been able to show that if G is cyclic, then H has at most n elements.
However, I can't go the other way. That is, assuming H has at most n elements, I haven't been able to say anything about whether G is cyclic, abelian or neither.
Any suggestions?
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