proof that $G$ is cyclic if and only if $\lvert G \rvert=\exp(G)$

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proof that $G$ is cyclic if and only if $\lvert G\rvert=\exp(G)$

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.

Type of Math Object:

Proof

Major Section:

Reference

Parent:

exponent

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Buddy list for rm50

Mathematics Subject Classification

20A99 None of the above, but in MSC2010 section 20Axx

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proof that $G$ is cyclic if and only if $\lvert G \rvert=\exp(G)$

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proof that $G$ is cyclic if and only if $\lvert G\rvert=\exp(G)$

Theorem 1.

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proof that $G$ is cyclic if and only if $\lvert G \rvert=\exp(G)$

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proof that GGG is cyclic if and only if |G|=exp⁡(G)GG\lvert G\rvert=\exp(G)

Theorem 1.

Mathematics Subject Classification

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proof that $G$ is cyclic if and only if $\lvert G\rvert=\exp(G)$