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On the difficulty of presenting finitely presentable groups

Abstract:

We exhibit classes of groups in which the word problem is uniformly solvable but in which there is no algorithm that can compute finite presentations for finitely presentable subgroups. Direct products of hyperbolic groups, groups of integer matrices, and right-angled Coxeter groups form such classes. We discuss related classes of groups in which there does exist an algorithm to compute finite presentations for finitely presentable subgroups. We also construct a finitely presented group that ...

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Publication status:
Published

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Publisher copy:
10.4171/GGD/129

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
GROUPS GEOMETRY AND DYNAMICS
Volume:
5
Issue:
2
Pages:
301-325
Publication date:
2010-03-26
DOI:
EISSN:
1661-7215
ISSN:
1661-7207
URN:
uuid:6edea9ac-60b0-42fc-a631-ab6064ed149d
Source identifiers:
132419
Local pid:
pubs:132419
Language:
English
Keywords:

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