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Free Crossed Resolutions of Groups and Presentations of Modules of Identities among Relations

Published online by Cambridge University Press:  01 February 2010

Ronald Brown  and
Abdul Razak Salleh
Ronald Brown
Affiliation:
School of Mathematics, University of Wales, Dean Street, Bangor, Gwynedd LL57 1UT, U.K., r.brown@bangor.ac.uk http://www.bangor.ac.uk/~mas010
Abdul Razak Salleh
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor D.E., Malaysia, aras@pkrisc.cc.ukm.my

Abstract

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The 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.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 2 , 1999 , pp. 28 - 61
Copyright
Copyright © London Mathematical Society 1999

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