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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 | ||
| عنوان مقاله [English] | ||
| Generalized Baer-Invariant of a Pair of Groups and the Direct Limit | ||
| نویسندگان [English] | ||
| M.R. Rismanchian | ||
| چکیده [English] | ||
| 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. | ||
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