关于凯格尔-维兰德的$\sigma$$问题

Pub Date : 2023-12-01 DOI:10.1134/s0081543823060093

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引用次数: 0

摘要

摘要对于所有素数集 $\mathbb{P}$的任意分割 $\sigma$，给出了有限群的子群的 $\sigma$-次正态性的充分条件。证明了 Kegel-Wielandt $\sigma$ - 问题在所有有限群的类中有一个正解，这些有限群的所有非标注组成因子都是交替群、零星群或秩为 1 的李群。

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On the Kegel–Wielandt $$\sigma$$ -Problem

Abstract

For an arbitrary partition $\sigma$ of the set $\mathbb{P}$ of all primes, a sufficient condition for the $\sigma$ -subnormality of a subgroup of a finite group is given. It is proved that the Kegel–Wielandt $\sigma$ -problem has a positive solution in the class of all finite groups all of whose nonabelian composition factors are alternating groups, sporadic groups, or Lie groups of rank 1.

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