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

Duncan, A. J. ; Ellis, Graham J. ; Gilbert, N. D.

Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 159-171

Résumé

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 M ∩ N. 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.

Détail

DOI : 10.1017/S0017089500031062

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