数学杂志2000，Vol.20Issue(1)：55-59,5.
有限Abel群的一个特征
A CHARACTERISTIC OF FINITE ABELIAN GROUPS
王俊新1
作者信息
- 1. 山西财经大学成人教育学院,太原,030012
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摘要
Abstract
In this paper,it is shown that a finite group G is abelian if and only if G satisfies the following conditions:(Ⅰ) G has a power automorphism α such that CG(α) is an elementary abelian 2-group.(Ⅱ) G has no subgroup isomorphic to 2-group <a,b|a2n=b2m=1,ab=a1+2n-1>where n≥3 and n≥m.In addition, applying the above result, the author also proves that if a finite group G has a power automorphism α such that CG(α) is an elementary abelian 2-group, then G is nilpotent.关键词
幂自同构/内-Σ群Key words
power automorphism/inner-∑group分类
数理科学引用本文复制引用
王俊新..有限Abel群的一个特征[J].数学杂志,2000,20(1):55-59,5.
