On finite groups with generalized σ-subnormal Schmidt subgroups

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.

KEYWORDS:

• σ-Nilpotent group
• finite group
• generalized σ-subnormal subgroup
• modular subgroup
• Schmidt subgroup

2010 Mathematics Subject Classification:

• 20D10
• 20D15