| Autor: |
Hamish Short, Gilbert Baumslag, Charles F. Miller, Martin R. Bridson |
| Jazyk: |
angličtina |
| Rok vydání: |
2016 |
| Předmět: |
|
| DOI: |
10.1007/s000140050136 |
| Popis: |
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 \( \pi_1 X \). |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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