ISSN:
1420-8946
Keywords:
Keywords. Finitely presented groups, fibre products, decision problems, non-positive curvature, hyperbolic groups, automatic groups.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. We give a criterion for fibre products to be finitely presented and use it as the basis of a construction that encodes the pathologies of finite group presentations into pairs of groups $ P \subset G $ where G is a product of hyperbolic groups and P is a finitely presented subgroup. This enables us to prove that there is a finitely presented subgroup P in a biautomatic group G such that the generalized word problem for $ P \subset G $ is unsolvable and P has an unsolvable conjugacy problem. An additional construction shows that there exists a compact non-positively curved polyhedron X such that $ \pi_1 X $ is biautomatic and there is no algorithm to decide isomorphism among the finitely presented subgroups of $ \pi_1 X $ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s000140050136
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