On the lattice of the σ-permutable subgroups of a finite group

2017/03/06 by Alexander N. Skiba, Skiba, Alexander N.
Computer Science · Engineering · Mathematics · #20D10 #20D30 #20E15 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · doi:10.48550/arxiv.1703.01773

openalex publication_date 2017/03/06 · openalex created_date 2021/12/06 · openalex updated_date 2026/07/28

Abstract

Let σ=\σ_i | i∈ I\ be some partition of the set of all primes ℙ, G a finite group and σ(G) =\σ_i |σ_i∩ π(G)≠ ∅ \. 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 σ_i∈ σ and \cal H contains exactly one Hall σ_i-subgroup of G for every σ_i∈ σ(G). A subgroup A of G is said to be σ-permutable in G if G possesses a complete Hall σ-set and A permutes with each Hall σ_i-subgroup H of G, that is, AH=HA for all i ∈ I. We characterize finite groups with distributive lattice of the σ-permutable subgroups.

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