Timeline for Presentation of special linear group over localizations of the integers
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 17 at 11:00 | answer | added | Carl-Fredrik Nyberg Brodda | timeline score: 7 | |
| Jan 17 at 10:48 | comment | added | Carl-Fredrik Nyberg Brodda | Note: Behr & Mennicke's paper actually gives $n=2$ and all prime $k$, not just $k=2$. | |
| Jun 20, 2018 at 7:10 | vote | accept | ahulpke | ||
| Jun 19, 2018 at 15:24 | answer | added | Matthias Wendt | timeline score: 7 | |
| Jun 18, 2018 at 20:38 | comment | added | Luc Guyot | Maybe "settles" is wrong. Serre recovered the presentations of Behr and Mennick for $n = 2$ and $k = 2, 3$ in "Cohomologie des groupes discrets", 1969. Those presentations seem to be the only explicit presentations at that time. (L&S mention that Proposition 13.1 can be used to compute presentations, but it becomes soon "unwieldy", even in the simplest cases). | |
| Jun 18, 2018 at 20:07 | comment | added | Luc Guyot | Proposition 13.3 of Lyndon & Schupp's "Combinatorial Group Theory" settles the case $n = 2$ and $k$ is any prime number. The result is attributed to Yasutaka Ihara, "On discrete subgroups of the two by two projective linear group over $\mathfrak{p}$ -adic fields", 1966. (I presume that it can be inferred from Remark 3 and §5 where the structure of $PGL(2, \mathbb{Q}_p))$ as an amalgam is given. | |
| Jun 18, 2018 at 14:16 | history | edited | ahulpke |
Added general group theory tag
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| Jun 17, 2018 at 19:51 | history | edited | ahulpke | CC BY-SA 4.0 |
Corrected localization as pointed out in comment.
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| Jun 17, 2018 at 19:49 | comment | added | ahulpke | @JulianRosen Yes, will correct. | |
| Jun 17, 2018 at 19:46 | comment | added | Julian Rosen | The set $\frac{1}{k}\mathbb{Z}$ is not a ring. Do you want $\mathbb{Z}[1/k]$ | |
| Jun 17, 2018 at 19:19 | history | asked | ahulpke | CC BY-SA 4.0 |