c-subnormality 子群对有限群结构的影响

Pub Date : 2024-06-25 DOI:10.1515/gmj-2024-2036

Dana Jaraden, Ali Ateiwi, Jehad Jaraden

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引用次数: 0

摘要

如果存在一个 G 的子正则子群 T，使得 H T = G {HT=G}，并且 H ∩ T ⩽ H G {H\cap T\leqslant H_{G}} ，我们就说 H 在 G 中是 c 正则子群。本文研究了在所有最大子群都是 c-subnormal 子群的假设下有限群 G 的结构，并提出了一些新的超可溶条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The influence of c-subnormality subgroups on the structure of finite groups

Let H be a subgroup of a group G. We say that H is c-subnormal in G if there exists a subnormal subgroup T of G such that H ⁢ T = G

{HT=G}

and H ∩ T ⩽ H G

{H\cap T\leqslant H_{G}}

, where H G

{H_{G}}

is the maximal normal subgroup of G which is contained in H. In this paper, we investigate the structure of a finite group G under the assumption that all maximal subgroups are c-subnormal subgroups and present some new conditions for supersolvability.

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