Abstract
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 algebraicK -theory, 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 homomorphism.
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Ellis, G. The Schur Multiplier of a Pair of Groups. Applied Categorical Structures 6, 355–371 (1998). https://doi.org/10.1023/A:1008652316165
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DOI: https://doi.org/10.1023/A:1008652316165