具有亚正态或模态施密特𝑝-𝑑-子群的群

Pub Date : 2024-02-09 DOI:10.1515/jgth-2023-0096

Victor S. Monakhov, Irina L. Sokhor

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引用次数: 0

摘要

施密特群是一个有限非零能群，它的每个适当子群都是零能的。在本文中，我们证明了如果有限群𝐺 的每个施密特子群都是子常群或模群，那么 G / F ( G ) G/F(G) 是循环群。此外，对于给定素数𝑝，我们描述了具有阶可被𝑝整除的亚正态或模态施密特子群的有限群的结构。

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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Groups with subnormal or modular Schmidt 𝑝𝑑-subgroups

A Schmidt group is a finite non-nilpotent group such that every proper subgroup is nilpotent. In this paper, we prove that if every Schmidt subgroup of a finite group 𝐺 is subnormal or modular, then G / F ⁢ ( G )

G/F(G)

is cyclic. Moreover, for a given prime 𝑝, we describe the structure of finite groups with subnormal or modular Schmidt subgroups of order divisible by 𝑝.

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