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单词 ProofThatGIsCyclicIfAndOnlyIflvertGrvertexpG
释义

proof that G is cyclic if and only if \\delimiter69640972G\\delimiter86418188=exp(G)


Theorem 1

A finite abelian group G is cyclic if and only if |G|=exp(G).

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.

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