On factorized groups

Abstract

The effect on a finite group G by the imposition of the condition that G is factorized by each of its maximal subgroups has been studied by Huppert, Deskins, Kegel, and others. In this paper, the effect on G brought about by the condition that G is factorized by a normalizer of a Sylow p-subgroup for each p ∈ π ( G ) p \in \pi (G) is studied. Through an extension of a classical theorem of Burnside, it is shown that certain results in the case where the factors are maximal subgroups continue to hold under the new conditions. Definite results are obtained in the case where the supplements of the Sylow normalizers are cyclic groups of prime power order or are abelian Hall subgroups of G.