The Generalization of the Stallings Theorem

Abstract

In this paper, we present a relative version of the concept of lower marginal series and give some isomorphisms among $\mathcal{V}G$-marginal factor groups. Also, we conclude a generalized version of the Stalling’s theorem. Finally, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite groups divides the order of the generalized Baer-invariant of its factor groups.