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

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


Glasgow Math. J., 37 (1995), no. 2, 159--171. ISSN 0017--0895


We obtain an eleven-term exact sequence in the low-dimensional homology of groups by means of mapping cone constructions on classifying spaces. Properties of the sequence are related to the notion of independence of normal subgroups and are used to deduce decomposition of relation modules for presentations with independent relation subgroups. Detailed consideration is given to independence of relation subgroups in presentations of one-relator products.

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Andrew Duncan
19 May 1999