Applied Categorical Structures

, Volume 6, Issue 3, pp 355–371 | Cite as

The Schur Multiplier of a Pair of Groups

  • Graham Ellis


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.

Schur multiplier relative central extension pair of groups 


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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Graham Ellis
    • 1
  1. 1.Department of Pure MathematicsUniversity College GalwayGalwayIreland

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