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Results tagged with decidability
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user 120914
12
votes
1
answer
406
views
Commutator problem vs conjugacy/word problem
In 1981, Comerford & Edmunds [1] asked whether decidability of the commutator problem for $G$ implies decidability of the conjugacy problem, or even the word problem, for $G$. …
7
votes
0
answers
285
views
Uniform word problem in finitely presented simple groups
The following question arose in the comments on this question, and it seems like a reasonable question to ask in its own right. I've added some additional details.
The word problem in any fixed finite …
8
votes
0
answers
121
views
The conjugacy problem for two-relator groups
The word problem for two-relator groups is a famous open problem (appearing e.g. as Question 9.29 in the Kourovka notebook), and decidability of the conjugacy problem implies decidability of the word problem … However, decidability of the conjugacy problem is not inherited by subgroups in general, so this does not answer the question. …
11
votes
Accepted
Reference request: Recent progress on the conjugacy problem for torsion-free one-relator gro...
As mentioned in the comments, this is still considered an open problem. I thought I'd flesh out a few aspects. A solution was claimed in 1992 by Juhasz, but it seems to have failed to convince experts …
18
votes
1
answer
750
views
Is solvability semi-decidable?
Let $G = \langle A \mid R \rangle$ be a finitely presented group, given by a finite presentation. If $G$ is abelian, then we can verify this fact: simply verify the fact that $[a, b] = 1$ for all gene …