On the Schur pair of groups. (English) Zbl 1463.20048
Summary: 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.
MSC:
20E10 | Quasivarieties and varieties of groups |
20C25 | Projective representations and multipliers |
20F50 | Periodic groups; locally finite groups |