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.
Rismanchian,M . (2011). Generalized Baer-Invariant of a Pair of Groups and the Direct Limit. Journal of Sciences, Islamic Republic of Iran, 22(2), 159-164.
MLA
Rismanchian,M . "Generalized Baer-Invariant of a Pair of Groups and the Direct Limit", Journal of Sciences, Islamic Republic of Iran, 22, 2, 2011, 159-164.
HARVARD
Rismanchian M. (2011). 'Generalized Baer-Invariant of a Pair of Groups and the Direct Limit', Journal of Sciences, Islamic Republic of Iran, 22(2), pp. 159-164.
CHICAGO
M Rismanchian, "Generalized Baer-Invariant of a Pair of Groups and the Direct Limit," Journal of Sciences, Islamic Republic of Iran, 22 2 (2011): 159-164,
VANCOUVER
Rismanchian M. Generalized Baer-Invariant of a Pair of Groups and the Direct Limit. J. Sci. I. R. I.. 2011;22(2):159-164.
Journal of Sciences, Islamic Republic of Iran