- #1

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_{4}.

I was able to show that it is Abelian through pairing the permutations, but my mind stopped at the noncyclic part. When showing that a group is cyclic or noncyclic, what exactly do I have to show?

- Thread starter Gear300
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- #1

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I was able to show that it is Abelian through pairing the permutations, but my mind stopped at the noncyclic part. When showing that a group is cyclic or noncyclic, what exactly do I have to show?

- #2

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A cyclic group is generated by a single element.

- #3

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Therefore, any one of those elements should be able to generate the others, right?

- #4

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In order to show a group is cyclic, one must find such a member

I'd look at (1 2)(3 4) and see if one can show whether it is a power of any of the others.

--Elucidus

- #5

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Does n have to be non-negative (in order for it to be a group, shouldn't n also be inclusive of negative integers - to identify the inverses)?

- #6

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Hope that helps!

- #7

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Thanks for the help.^{2}=1. However, the order of the group is 4, and so no single element can generate the group. Thus the group is not cyclic.

Hope that helps!

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