On the partial Π-property of second minimal or second maximal subgroups of Sylow subgroups of finite groups

2023/04/22 by Zhengtian Qiu, Jianjun Liu, Qiu, Zhengtian +3
Mathematics · Medicine · #Chronic Myeloid Leukemia Treatments #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2304.11451

openalex publication_date 2023/04/22 · openalex created_date 2023/04/27 · 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 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 study the influence of some second minimal or second maximal subgroups of a Sylow subgroup satisfying the partial Π-property on the structure of a finite group.

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