Bridson, Martin R. and Wilton, Henry (2011) On the difficulty of presenting finitely presentable groups. Groups, Geometry, and Dynamics, 5 (2). pp. 301-325. ISSN 1661-7207 http://resolver.caltech.edu/CaltechAUTHORS:20110412-104051639
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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.
|Additional Information:||© 2010 European Mathematical Society. Received March 25, 2010; revised July 30, 2010. Bridson is supported by a Senior Fellowship from the EPSRC. Wilton is supported in part by NSF grant DMS-0906276.|
|Subject Keywords:||Finitely presentable groups, hyperbolic groups, linear groups, decision problems|
|Classification Code:||Mathematics Subject Classification (2010): 20F10, 20F65, 20F67|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||23 Jun 2011 16:52|
|Last Modified:||23 Jun 2011 16:52|
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