On finite groups factorized by σ-nilpotent subgroups

2021/04/18 by Zhenfeng Wu, Chi Zhang, Wu, Zhenfeng +1
Computer Science · Engineering · Mathematics · #20D10 #20D15 #20D20 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2104.08788

openalex publication_date 2021/04/18 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group and σ=\σ_i|i∈ I\ be a partition of the set of all primes ℙ, that is, ℙ=\bigcup_{i∈ I}σ_i and σ_i∩ σ_j=∅ for all i≠ j. A chief factor H/K of G is said to be σ-central in G, if the semidirect product (H/K)\rtimes(G/C_G(H/K)) is a σ_i-group for some i∈ I. The group G is said to be σ-nilpotent if either G=1 or every chief factor of G is σ-central. In this paper, we study the properties of a finite group G=AB, factorized by two σ-nilpotent subgroups A and B, and also generalize some known results.

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