A sequence of factorizable subgroups

Abstract

Let \(G\) be a non-abelian non-simple group. In this article the group \(G\) such that \(G=MC_G(M)\) will be studied, where \(M\) is a proper maximal subgroup of \(G\) and \(C_G(M)\) is the centralizer of \(M\) in \(G\).