On a product of two formational 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 Y ≤ T there exists an element u ∈ hX, Y i such that XYᵘ ≤ G. The notation H ≤ G means that H is a subgroup of a group G. In this paper we consider a group G = AB such that A and B are tcc-subgroups in G. We prove that G belongs to F, when A and B belong to F and F is a saturated formation of soluble groups such that U ⊆ F. Here U is the formation of all supersoluble groups.