Finite groups with some subgroups satisfying the partial Π-property

2023/11/21 by Zhengtian Qiu, Qiu, Zhengtian, Guiyun Chen +3
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2311.12633

openalex publication_date 2023/11/21 · openalex created_date 2023/11/24 · openalex updated_date 2026/07/28

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 =G₀ < G₁ < ⋅⋅⋅ < G_n= G of G such that for every G -chief factor G_i/G_i-1 (1≤ i≤ n) of \varGamma_G , | G / G_i-1 : N _G/G_i-1 (HG_i-1/G_i-1∩ G_i/G_i-1)| is a π(HG_i-1/G_i-1∩ 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.

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