On a generalisation of finite T-groups

2020/07/22 by Chi Zhang, Wenbin Guo, Zhang, Chi +1
Computer Science · Engineering · Mathematics · #20D10 #20D15 #20D20 #20D35 #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.2007.11288

openalex publication_date 2020/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let σ=\σ_i |i∈ I\ is some partition of all primes ℙ and G a finite group. A subgroup H of G is said to be σ-subnormal in G if there exists a subgroup chain H=H₀≤ H₁≤ ⋯ ≤ H_n=G such that either H_i-1 is normal in H_i or H_i/(H_i-1)_Hi is a finite σ_j-group for some j ∈ I for i = 1, …, n. We call a finite group G a T_σ-group if every σ-subnormal subgroup is normal in G. In this paper, we analyse the structure of the T_σ-groups and give some characterisations of the T_σ-groups.

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