On one generalization of finite \frak U-critical groups

2014/12/17 by V. N. Semenchuk, Vladimir N. Semenchuk, Semenchuk, Vladimir N. +2
Computer Science · Mathematics · #20D10 #20D15 #20D20 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20D10 #msc:20D15 #msc:20D20

paper · pdf · doi:10.48550/arxiv.1412.5469

arxiv created 2014/12/17 · openalex publication_date 2014/12/17 · arxiv updated 2014/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A proper subgroup H of a group G is said to be: ℙ-subnormal in G if there exists a chain of subgroups H=H₀ < H₁< ... < H_n=G such that |H_i:H_i-1| is a prime for i=1,...,n; ℙ-abnormal in G if for every two subgroups K≤ L of G, where H≤ K, |L:K| is not a prime. In this paper we describe finite groups in which every non-identity subgroup is either ℙ-subnormal or ℙ-abnormal.

Related

• On K-ℙ_t-subnormal subgroups of finite groups and related formations
• Finite groups with \Bbb P-subnormal 2-maximal subgroups
• Finite groups with \mathbb P-subnormal primary cyclic subgroups
• On a generalisation of finite T-groups
• On K\mathfrak F-subnormality and submodularity in a finite group