Decision problems and profinite completions of groups
| dc.creator | Bridson, Martin R. | |
| dc.date | 2008-10-02 | |
| dc.date.accessioned | 2026-07-07T10:07:04Z | |
| dc.date.available | 2026-07-07T10:07:04Z | |
| dc.description | We consider pairs of finitely presented, residually finite groups $P\hookrightarrow\G$ for which the induced map of profinite completions $\hat P\to \hat\G$ is an isomorphism. We prove that there is no algorithm that, given an arbitrary such pair, can determine whether or not $P$ is isomorphic to $\G$. We construct pairs for which the conjugacy problem in $\G$ can be solved in quadratic time but the conjugacy problem in $P$ is unsolvable. Let $\mathcal J$ be the class of super-perfect groups that have a compact classifying space and no proper subgroups of finite index. We prove that there does not exist an algorithm that, given a finite presentation of a group $\G$ and a guarantee that $\G\in\mathcal J$, can determine whether or not $\G\cong\{1\}$. We construct a finitely presented acyclic group $\H$ and an integer $k$ such that there is no algorithm that can determine which $k$-generator subgroups of $\H$ are perfect. | |
| dc.identifier | https://arxiv.org/abs/0810.0390 | |
| dc.identifier | http://arxiv.org/abs/0810.0390 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170507 | |
| dc.subject | Group Theory | |
| dc.subject | 20E18, 20F10 | |
| dc.title | Decision problems and profinite completions of groups | |
| dc.type | text |