Year: 2023
Type: preprint
Abstract: Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the partial $ Π$-property in $ G $ if there exists a chief series $ \varGamma_{G}: 1 =G_{0} < G_{1} < \cdot\cdot\cdot < G_{n}= G $ of $ G $ such that for every $ G $-chief factor $ G_{i}/G_{i-1} $ $(1\leq i\leq n) $ of $ \varGamma_{G} $, $ | G / G_{i-1} : N _{G/G_{i-1}} (HG_{i-1}/G_{i-1}\cap G_{i}/G_{i-1})| $ is a $ π(HG_{i-1}/G_{i-1}\cap G_{i}/G_{i-1}) $-number. In this paper, we investigate how some subgroups satisfying the partial $Π$-property influence the structure of finite groups.
Source: arXiv (Cornell University)
Authors: Qiu, Zhengtian, Chen, Guiyun, Liu, Jianjun
Institution: Southwest University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4388962812