The Schur multiplier of a pair of groups

Graham Ellis

doi:10.1023/A:1008652316165

The Schur multiplier of a pair of groups

Graham Ellis

Mathematics

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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 algebraic K-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.

Original language	English
Pages (from-to)	355-371
Number of pages	17
Journal	Applied Categorical Structures: A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science
Volume	6
Issue number	3
DOIs	https://doi.org/10.1023/A:1008652316165
Publication status	Published - Sep 1998

Keywords

Pair of groups
Relative central extension
Schur multiplier

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10.1023/A:1008652316165

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AB - 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 K-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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KW - Relative central extension

KW - Schur multiplier

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JF - Applied Categorical Structures: A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science

IS - 3

ER -

The Schur multiplier of a pair of groups

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