On the IC-Π-property of subgroups of finite groups

2025/10/09 by Zhengtian Qiu, Qiu, Zhengtian, S Qiao +1
Mathematics · #Finite Group Theory Research #Rings, Modules, and Algebras #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2510.08426

Abstract

Let H be a subgroup of a finite group G . We say that H satisfies the Π-property in G if | G/K : N_G/K((H ∩ L)K/K)| is a π(( H ∩ L)K/K ) -number for any chief factor L/K of G ; and we call that H satisfies the IC - Π-property in G if H∩ [H, G] satisfies the Π-property in G . In this paper, we obtain a criterion of a normal subgroup being contained in the p\mathfrakU -hypercenter of a finite group by the IC- Π-property of some p -subgroups.

Citations

• Finite groups with generalized Ore supplement conditions for primary subgroups

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