Computing subgroup presentations, using the coherence
arguments of McCammond and Wise
Oliver Payne and Sarah Rees,\
Keywords subgroup presentation coherence 2-complex
Status 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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