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AbstractThe paper gives formulae for a module presentation of the module of identities among relations for a presentation of a group, in terms of information on 0- and 1-combings of the Cayley graph. These formulae are seen as a special case of formulae for extending a partial free crossed resolution of a group, given a partial contracting homotopy of the universal cover of the partial resolution.doi:10.1112/s1461157000000061 fatcat:rteyjsmygrbofbkzk3dgz45uma