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Some inequalities for the Baer-invariant of a pair of finite groups |
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| Authors: | Mohammad Reza R. Moghaddam Ali Reza Salemkar Hossein M. Saanye |
| Affiliation: | a Department of Mathematics, Islamic Azad University of Mashhad and Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Iran b Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran c Department of Mathematics, Valiasr University, Rafsanjan, Iran |
| Abstract: | In this paper we introduce the concept of Baer-invariant of a pair of groups with respect to a variety of groups v. Some inequalities for the Baer-invariant of a pair of finite groups are obtained, when v is considered to be the Schur-Baer variety. We also present a condition for which the order of the Baerinvariant of a pair of finite groups divides the order of the Baer-invariant of their factor groups. Finally, some inequalities for the Schur-multiplier of a pair of finite nilpotent groups and their factor groups are given. |
| Keywords: | 20E10 20D15 20F18 |
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