On one generalization of modular subgroups

2017/08/11 by Jianhong Huang, Bin Hu, Huang, Jianhong +3
Computer Science · Mathematics · #20D10 #20D15 #20D20 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1708.03550

openalex publication_date 2017/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group. If M_n < M_n-1 < … < M₁ < M₀=G where M_i is a maximal subgroup of M_i-1 for all i=1, … ,n, then M_n (n > 0) is an n-maximal subgroup of G. A subgroup M of G is called modular if the following conditions are held: (i) ⟨ X, M ∩ Z ⟩=⟨ X, M ⟩ ∩ Z for all X ≤ G, Z ≤ G such that X ≤ Z, and (ii) ⟨ M, Y ∩ Z ⟩=⟨ M, Y ⟩ ∩ Z for all Y ≤ G, Z ≤ G such that M ≤ Z. In this paper, we study finite groups whose n-maximal subgroups are modular.

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