On numerical invariants of a finite group factorized by tcc-subgroups

Abstract

A subgroup A of a group G is called tcc-subgroup in G, if there is a subgroup T of G such that G = AT and for any X ≤ A and for any Y ≤ T there exists an element u ∈ ⟨X; Y ⟩ such that XY ^u ≤ G. The notation H ≤ G means that H is a subgroup of a group G. In this paper, we obtained the estimations of numerical invariants(the derived length, the nilpotent length, the π-length, the nilpotent π-length) of G = AB in terms of invariants of tcc-subgroups A and B.