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[parent] proof that $G$ is cyclic if and only if $\lvert G \rvert=\exp(G)$ (Proof)
Theorem 1   A finite abelian group $G$ is cyclic if and only if $\lvert G\rvert=\exp(G)$
Proof. $G$ is cyclic if and only if it has an element of order $\lvert G\rvert$ But $\exp(G)$ is the maximum order of any element of $G$ Thus $G$ is cyclic only if these two are equal.



"proof that $G$ is cyclic if and only if $\lvert G \rvert=\exp(G)$" is owned by rm50.
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Cross-references: order, proof, cyclic, abelian group, finite

This is version 3 of proof that $G$ is cyclic if and only if $\lvert G \rvert=\exp(G)$, born on 2007-01-14, modified 2007-01-14.
Object id is 8759, canonical name is GIsCyclicIfAndOnlyIfLvertGrvertexpG.
Accessed 900 times total.

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AMS MSC: 20A99 (Group theory and generalizations :: Foundations :: Miscellaneous)
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