In this article we develop the theory of a Schur multiplier for “pairs of groups”. The idea of such a multiplier is implicit in the work of J.-L. Loday (1978) and others on algebraic Ktheory, and in the work of Eckmann et al. (1972) and others on group homology. In contrast to their work, we focus on the general group-theoretic properties of the multiplier. These properties are systematically derived from: 1) the functoriality of the multiplier; 2) an exact homology sequence; 3) and a transfer… CONTINUE READING