Finite groups with permutable Hall subgroups

2017/02/11 by Xia Yin, Nanying Yang, Yin, Xia +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1702.03371

openalex publication_date 2017/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let σ=\σ_i | i∈ I\ be a partition of the set of all primes ℙ and G a finite group. A set \cal H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of \cal H is a Hall σ_i-subgroup of G for some i∈ I and \cal H contains exactly one Hall σ_i-subgroup of G for every i such that σ_i∩ π(G)≠ ∅. In this paper, we study the structure of G assuming that some subgroups of G permutes with all members of \cal H.

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