关于所有最小子群都是 BNA 子群的有限群

Yanhui Wang, Xiuyun Guo
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引用次数: 0

摘要

- 如果 𝐻 𝑥 = 𝐻 或 𝑥 ∈ ⟨ 𝐻, 𝐻 𝑥 ⟩ 对于所有 𝑥 ∈ 𝐺 都是,则称𝐵𝑁𝐴-子群。本文的目的首先是给出如果 𝐺 的所有最小子群都是𝐵𝑁𝐴 - 𝐺 的子群时 𝐺 的拟合高度的最佳约束,其次是回答本文的问题 [On 𝐵𝑁𝐴 -normality and solvability of finite groups, Rend.Sem.Mat.Padova 136 (2016), 51-60].最后,我们利用少数𝐵𝑁𝐴-素阶子群来确定有限群的结构。事实上,我们已经给出了有限群可超溶的一些新条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On finite groups in which all minimal subgroups are BNA-subgroups
– A subgroup 𝐻 of a group 𝐺 is said to be a 𝐵𝑁𝐴 -subgroup of 𝐺 if either 𝐻 𝑥 = 𝐻 or 𝑥 ∈ ⟨ 𝐻, 𝐻 𝑥 ⟩ for all 𝑥 ∈ 𝐺 . The purpose of this paper is first to give the best bound for the Fitting height of 𝐺 if all minimal subgroups of 𝐺 are 𝐵𝑁𝐴 -subgroups of 𝐺 , and next give an answer for the question of the paper [On 𝐵𝑁𝐴 -normality and solvability of finite groups, Rend. Sem. Mat. Univ. Padova 136 (2016), 51-60]. Finally we use few 𝐵𝑁𝐴 -subgroups of prime order to determine the structure of the finite groups. In fact, some new conditions for a finite group to be supersolvable have been given.
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