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Results tagged with profinite-groups
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user 1463
10
votes
Is there a residually finite non-elementary hyperbolic group whose profinite completion is b...
I'm fairly certain that no example is known. Of course, it's a famous open problem whether every hyperbolic group is residually finite. This turns out to be equivalent to many other questions about t …
- 25.2k
3
votes
Are braid groups conjugacy separable?
(26 April 2016: Updated to give a fuller answer.)
I'm fairly confident this question is still open.
As Ian Agol points out in comments, the 3-strand braid group is, by a happy accident, also the fun …
- 25.2k
4
votes
Accepted
Bases of free groups
As Derek Holt says in comments, the answer to your first question is 'yes'. You can argue topologically.
There is a rose $R$ corresponding to $X$ with $\pi_1R\cong F$. The subset $A$ defines a conn …
- 25.2k
12
votes
Accepted
A hyperbolic group with a small profinite completion
It's a famous open question whether every word-hyperbolic group is residually finite. Kapovich--Wise showed that this is equivalent to asking whether every non-trivial word-hyperbolic group has non-t …
- 25.2k
5
votes
An algebraic approach to the thermodynamic limit $N\rightarrow\infty$?
I doubt the following has anything to do with the thermodynamic limit. However, it has been pointed out that neither the inverse nor the projective limit of a sequence of $\mathbb{Z}/N$'s gives you $ …
- 25.2k