Author

• M.R. Rismanchian

Department of Mathematics, Faculty of Sciences, University of Shahre-Kord

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.

Keywords

• Generalized Baer-invariant
• Verbal and marginal subgroups
• Pair of groups
• Direct limit