Generalized Baer-Invariant of a Pair of  Groups and the Direct Limit

	Generalized Baer-Invariant of a Pair of Groups and the Direct Limit
Journal of Sciences, Islamic Republic of Iran
مقاله 9، دوره 22، شماره 2، شهریور 2011، صفحه 159-164 اصل مقاله (313.15 K)
نویسنده
M.R. Rismanchian
Department of Mathematics, Faculty of Sciences, University of Shahre-Kord
چکیده
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.
کلیدواژه‌ها
Generalized Baer-invariant؛ Verbal and marginal subgroups؛ Pair of groups؛ Direct limit

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