On the Schur pair of groups

Document Type : Research Paper

Author

Department of mathematics, Faculty of Sciences, Golestan University, Gorgan.

10.29252/as.2020.1686

Abstract

In this paper, it is shown that $ (\mathcal{V}, \mathfrak{X}) $ is a Schur pair if and only if the Baer-invariant of an $\mathfrak{X}$-group with respect to $ \mathcal{V}$ is an $\mathfrak{X}$-group. Also, it is proved that a locally $\mathfrak{X}$ class inherited the Schur  pair property of , whenever $\mathfrak{X}$ is closed with respect to forming subgroup, images and extensions of its members. Subsequently,  many interesting predicates  about some generalizations of Schur's theorem and Schur multiplier of groups will be concluded.

Keywords


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