- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:59
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
5
2011
2
On the difficulty of presenting finitely presentable groups
Martin
Bridson
University of Oxford, OXFORD, UNITED KINGDOM
Henry
Wilton
University of Cambridge, CAMBRIDGE, GREAT BRITAIN
Finitely presentable groups, hyperbolic groups, linear groups, decision problems
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 has a polynomial Dehn function but in which there is no algorithm to compute the first Betti number of its finitely presentable subgroups.
Group theory and generalizations
General
301
325
10.4171/GGD/129
http://www.ems-ph.org/doi/10.4171/GGD/129