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A Mayer-Vietoris sequence in group homology and the decomposition of relation modules

  • A. J. Duncan (a1), Graham J. Ellis (a2) and N. D. Gilbert (a3)

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W. A. Bogley and M. A. Gutierrez [2] have recently obtained an eight-term exact homology sequence that relates the integral homology of a quotient group Г/MN, where M and N are normal subgroups of the group Г, to the integral homology of the free product Г/M * Г/N in dimensions ≤3 by means of connecting terms constructed from commutator subgroups of Г, M, N and MN. In this paper we use the methods of [4] to recover this exact sequence under weaker hypotheses and for coefficients in /q for any non-negative integer q. Further, for q = 0 we extend the sequence by three terms in order to capture the relation between the fourth homology groups.

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References

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A Mayer-Vietoris sequence in group homology and the decomposition of relation modules

  • A. J. Duncan (a1), Graham J. Ellis (a2) and N. D. Gilbert (a3)

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