Timeline for Can the finiteness of a Burnside group with two generators be checked algorithmically by using Fuchsian von Dyck groups?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 9, 2014 at 4:10 | vote | accept | Giovanni Moreno | ||
| Sep 8, 2014 at 22:31 | comment | added | HJRW | @G_infinity, various experts on Burnside groups are (or have been) active on MO. Mark Sapir is one. The difference with the search for digits of $\pi$ or prime numbers is that these are finite problems: there are upper bounds on the time it will take to find the next one, and the task is to reduce the run time to something reasonable. On the other hand, if $B(2,5)$ is infinite then the algorithm I described will run forever. | |
| Sep 8, 2014 at 5:13 | comment | added | Giovanni Moreno | Your almost cleared out all my doubts - yet I need time to fully digest your answer. Now, let us focus on your last sentence: "I certainly don't see any particular obstruction to attempting the computation in the case of $B(2,5)$". Believe me, I've been trying for years to find out what is the state-of-the-art concerning the finiteness of $B(2,5)$, but in vain. Can you point out somebody to whom I may ask? Why there are a lot of computers employed to discover the 'last' digit of $\pi$, or the 'biggest' prime, but none cares about finiteness of $B(2,5)$? Is there at least the algorithm written? | |
| Sep 7, 2014 at 10:15 | comment | added | HJRW | Perhaps I should add something to explain the connection with the cited paper. Since $B(2,n)$ is a quotient of the von Dyck group $D(n,n,n)$, which is the fundamental group of a hyperbolic (for $n>3$) 2-orbifold $O$, you can replace $F$ by $D(n,n,n)$ and $X$ by $O$, and play the same game. | |
| Sep 7, 2014 at 8:49 | history | answered | HJRW | CC BY-SA 3.0 |