On finite groups with generalized σ-subnormal Schmidt subgroups. Issue 7 (3rd July 2018) - Hu, Bin; Huang, Jianhong
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.