In this article the author develops the theory of a Schur multiplier for pairs of groups and he shows that it leads to a more systematic treatment of a number of results on the usual multiplier. In several instances this treatment yields sharper results.
The Schur multiplier of the pair , where is a normal subgroup of , is defined as a functorial Abelian group whose principal feature is a natural exact sequence
(). The definition is given via classifying spaces of groups but a purely homological algebraic definition and proof of the exactness of the above sequence is also given by the author [in Glasg. Math. J. 29, 13-19 (1987; Zbl 0631.20040)].