On the Schur pair of groups

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.