On finite groups with generalized σ-subnormal Schmidt subgroups. Issue 7 (3rd July 2018)

• Record Type: Journal Article
• Authors: Hu, Bin; Huang, Jianhong
• Is Part Of: Communications in algebra. Volume 46:Issue 7(2018)
• Page Start: 3127
• Page End: 3134
• Publication Date: 2018-07-03
• Subjects: σ-Nilpotent group -- finite group -- generalized σ-subnormal subgroup -- modular subgroup -- Schmidt subgroup; 20D10 -- 20D15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1404091
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let G be a finite group and σ = { σ i | i ∈ I } some partition of the set of all primes. A subgroup A of G is said to be generalized σ -subnormal in G if A = ⟨ L, T ⟩, where L is a modular subgroup and T is a σ -subnormal subgroup of G . In this paper, we prove that if every Schmidt subgroup of G is generalized σ -subnormal in G, then the commutator subgroup G ′ of G is σ -nilpotent.