恰有14个非幂子群的群
对于群$G$和正整数$m\ge1$,记$G^m$表示由$G$中所有元素的$m$次幂生成的子群.那些无法表示为$G^m$形式的子群称为非幂子群.本文在已有对非幂子群个数不超过13的群的分类基础上,我们给出恰有14个非幂子群的群分类.
For a group $G$ and a positive integer $m\ge 1$, let $G^m$ denote the subgroup generated by the $m$ powers of all elements in $G$. Subgroups that cannot be expressed in the form $G^m$ are called nonpower subgroups. Building upon the existing classification of groups with at most 13 nonpower subgroups, we classify the finite groups with exactly 14 nonpower subgroups.
王淇、周伟
西南大学数学与统计学院,重庆 400715 西南大学数学与统计学院,重庆 400715
数学
子群计数\quad 幂子群\quad 非幂子群
counting subgroups power subgroups nonpower subgroups
王淇,周伟.恰有14个非幂子群的群[EB/OL].(2025-06-18)[2025-06-21].http://www.paper.edu.cn/releasepaper/content/202506-84.点此复制
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