On the partial \mathscr L - Π-property of subgroups of finite groups

2024/07/23 by Qiu, Zhengtian, Ballester-Bolinches, Adolfo
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2408.06348

Abstract

Let H be a subgroup of a finite group G . We say that H satisfies the partial \mathscr L - Π-property in G if H\unlhd G , or if | G / K : N _{G / K} (HK/K)| is a π(HK/K) -number for any G -chief factor of type H^G/K with H_G≤ K . In this paper, we investigate the structure of finite groups under the assumption that some subgroups of prime power order satisfy the partial \mathscr L - Π-property.

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