Intersection of maximal subgroups in prosolvable groups

2017/03/09 by Iker de las Heras, Heras, Iker de las, Andrea Lucchini +1
Engineering · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1703.03276

openalex publication_date 2017/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be an open subgroup of a profinite group that can be expressed as intersection of maximal subgroups of G. Given a positive real number η, we say that H is an η-intersection if there exists a family of maximal subgroups M₁,…,M_t such that H=M₁∩…∩ M_t and |G:M₁|⋯|G:M_t|≤ |G:H|^η. We investigate the meaning of this property and its influence on the group structure.

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