Author/Authors :
Rismanchian1، M.R. نويسنده 1Department of Mathematics, Faculty of Sciences, University of Shahre-Kord, Shahre-Kord, Islamic Republic of Iran , , Araskhan، M. نويسنده 2Department of Mathematics, University of Islamic Azad, Yazd Branch, Islamic Republic of Iran ,
Abstract :
In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, 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 a pair of their factor groups. Moreover, we prove that the generalized Baer-invariant of a pair of groups commutes with direct limit.
