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A generalised tensor product G 0 H of groups G, H has been introduced by R. Brown and J.-L. Loday in [3,4]. It arises in applications in homotopy theory of a generalised Van Kampen theorem. The reason why G 0 H does not necessarily reduce to GUh Oz Huh, the usual tensor product over Z of the abelianisations, is that it is assumed that G acts on H (on the(More)
In this note we generalise Hopfs formula for the second homology of a group G in terms of a free presentation R >-• F^» G. We prove: THEOREM 1. Let R lt ...,R n be normal subgroups of a group F such that F/Y\i iiin Ri = G, and for each proper subset A of <«> = {1,...,«} the groups H r (F/Y[ ieA R,) are trivial for r = 2ifA = 0, and for r = \A\ + 1 and \A\ +(More)
This work is devoted to an interpretation and computation of the first homology groups of the small category given by a rewriting system. It is shown that the elements of the first homology group may be regarded as the equivalence classes of the flows in a graph of the rewriting system. This is applied to calculating the homology groups of asynchronous(More)