Fibre products, non-positive curvature, and decision problems
Fibre products, non-positive curvature, and decision problems
复制标题
纤维产品、非正曲率和决策问题
DOI：
10.1007/s000140050136
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发表时间：
2000
影响因子：
0.9
通讯作者：
H. Short
中科院分区：
文献类型：
--
作者：
G. Baumslag;M. Bridson;Charles F. Miller;H. Short
我们给出了一个标准的纤维产品被cross-presented和使用它作为基础的建设，编码的病理有限群presentations成对groupswhere G是一个产品的双曲群和P是一个cross-presented子群。这使我们能够证明存在一个双自动群G的子群P_n，使得广义字问题为不可解，且P有一个共轭问题不可解。另一种构造证明了存在一个紧的非正曲多面体X，使得X是双自动的，并且没有算法来判定X的子群之间的同构。
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 groupswhereGis a product of hyperbolic groups andPis a finitely presented subgroup. This enables us to prove that there is a finitely presented subgroupPin a biautomatic groupGsuch that the generalized word problem foris unsolvable andPhas an unsolvable conjugacy problem. An additional construction shows that there exists a compact non-positively curved polyhedronXsuch thatis biautomatic and there is no algorithm to decide isomorphism among the finitely presented subgroups of.