On the Schur pair of groups

Document Type : Research Paper


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



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.


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