Timeline for Class number of Burnside groups
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 17, 2016 at 8:24 | comment | added | MSMalekan | @Jan-ChristophSchlage-Puchta: Your understanding of problem is correct. But I think a Tarski monsters are quotients of Burnside groups, aren't? | |
| Feb 17, 2016 at 8:08 | comment | added | MSMalekan | By a Burnside group $B(m,n)$, I mean the group $\langle x_1,\dotsc,x_n: w^n=1,\, w\text{ is a word in $x_i^{\pm1}$}\rangle$, not the quotient of this group. | |
| Feb 16, 2016 at 20:15 | comment | added | Jan-Christoph Schlage-Puchta | Oh, I read the question as "Suppose I can prove that $B(n,m)$ has finitely many conjugacy classes, can I deduce that $B(n,m)$ is finite?". A Tarski monster with finitely many conjugacy classes shows that this conclusion is not immediate. | |
| Feb 16, 2016 at 20:11 | comment | added | Yiftach Barnea | Jan-Christoph I think he meant that $B(m,n)$ is the free group of exponent $n$ on the $m$ generators. So to give a negative answer you need to find a group of exponent $n$ with $m$ generators which has infinite class number or a sequence of such groups which have unbounded class numbers. | |
| Feb 16, 2016 at 20:04 | history | answered | Jan-Christoph Schlage-Puchta | CC BY-SA 3.0 |