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.