Finite groups with some subgroups of prime power order satisfying the partial Π-property

2024/04/01 by Zhengtian Qiu, Qiu, Zhengtian, A. Ballester‐Bolinches +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2404.01254

openalex publication_date 2024/04/01 · openalex created_date 2025/10/10 · 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 G-chief series \varGamma_G: 1 =G₀ < G₁ < ⋅⋅⋅ < G_n= G of G such that | 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 for every G -chief factor G_i/G_i-1 of \varGamma_G , 1≤ i≤ n. In this paper, we investigate the structure of a finite group G under the assumption that some subgroups of prime power order satisfy the partial Π-property.

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