proof that $G$ is cyclic if and only if $69640972G86418188=exp(G)$

Theorem 1

A finite abelian group $G$ is cyclic if and only if $\mathrm{|}G\mathrm{|}\mathrm{=}\exp \mathit{}\mathrm{(}G\mathrm{)}$.

Proof. $G$ is cyclic if and only if it has an element of order $|G|$. But $\exp (G)$ is the maximum order of any element of $G$. Thus $G$ is cyclic only if these two are equal.

Title	proof that $G$ is cyclic if and only if $69640972G86418188=exp(G)$
Canonical name	ProofThatGIsCyclicIfAndOnlyIflvertGrvertexpG
Date of creation	2013-03-22 16:34:14
Last modified on	2013-03-22 16:34:14
Owner	rm50 (10146)
Last modified by	rm50 (10146)
Numerical id	6
Author	rm50 (10146)
Entry type	Proof
Classification	msc 20A99