On the Schur pair of groups

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:

Variety of groups , Class of groups , Schur pair property , Baer-invariant of groups