Computing subgroup presentations, using the coherence arguments of McCammond and Wise

Oliver Payne and Sarah Rees,\


subgroup presentation coherence 2-complex


Published in Journal of Algebra 300 (2006) 109-133


We describe an algorithm which may be used to compute a finite presentation of a finitely generated subgroup of a finitely presented group $G$, provided that $G$ satisfies appropriate hypotheses. The algorithm is based on an algorithm of McCammond and Wise, but is extended to cover a wider class of groups, including all those satisfying the path reduction or weak 2-cell reduction hypotheses of McCammond and Wise. The proofs of correctness of our algorithm emerge from McCammond and Wise' own proofs that their hypotheses imply coherence of the groups satisfying them. We also demonstrate that the algorithm may be extended further to cover groups satisfying appropriate conditions on fans (strings of 2-cells) within disc diagrams. The core of this work originally appeared in the PhD thesis of the first author.

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