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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
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
GROUPS GEOMETRY AND DYNAMICS
Volume:
5
Issue:
2
Pages:
301-325
Publication date:
2010-03-26
DOI:
EISSN:
1661-7215
ISSN:
1661-7207
Language:
English
Keywords:
Pubs id:
pubs:132419
UUID:
uuid:6edea9ac-60b0-42fc-a631-ab6064ed149d
Local pid:
pubs:132419
Source identifiers:
132419
Deposit date:
2012-12-19

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