Showing an Abelian group is cyclic

Asked Apr 12 '16 at 18:13

Active Apr 12 '16 at 18:18

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Can someone please give me a hint to prove that if the order of the group $|G|=6$ and $G$ is abelian, then $G$ is cyclic?

My idea: if G is of order 6, then say, $x\in G$, then $|x|=|\lt x \gt|=6$ , then $G $ is cyclic? I do not know if this is true

Thanks in advance!

asked Apr 12 '16 at 18:13

Frank Booth

1

See also http://lincoln.sjfc.edu/~gwildenberg/abstract_algebra/abelian-6.html. – lhf Apr 12 '16 at 18:24
@Ihf can you please help me understand a comment there? someone has commented that if $n=p_1...p_k$, where $p_i$ is prime, then the group is cyclic. – Frank Booth Apr 12 '16 at 18:25
may I ask in the chat @Ihf? – Frank Booth Apr 12 '16 at 18:27
@Ihf Ok, I am posting now. Thanks :) – Frank Booth Apr 12 '16 at 18:29
@Ihf I did http://math.stackexchange.com/questions/1739581/an-abelian-group-of-order-n-is-cyclic – Frank Booth Apr 12 '16 at 18:33

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