On finite groups with some primary subgroups satisfying partial S-Π-property

2015/07/31 by Xiaoyu Chen, Chen, Xiaoyu, Yuemei Mao +3
Computer Science · Engineering · Mathematics · #20D10 #20D20 #20D30 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR #msc:20D10 #msc:20D20 #msc:20D30

paper · pdf · doi:10.48550/arxiv.1507.08951

arxiv created 2015/07/31 · openalex publication_date 2015/07/31 · arxiv updated 2015/08/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A p-subgroup H of a finite group G is said to satisfy partial S-Π-property in G if G has a chief series Γ_G: 1=G₀<G₁<⋯<G_n=G such that for every G-chief factor G_i/G_i-1 (1\leqslant i\leqslant n) of Γ_G, either (H∩ G_i)G_i-1/G_i-1 is a Sylow p-subgroup of G_i/G_i-1 or |G/G_i-1: N_G/G_i-1((H∩ G_i)G_i-1/G_i-1)| is a p-number. In this paper, we mainly investigate the structure of finite groups with some primary subgroups satisfying partial S-Π-property.

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