Timeline for Relations between two particular elements of SL_2(Z)?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 18, 2010 at 22:04 | comment | added | Victor Miller |
First you should work in $PSL_2(\mathbb{Z})$ just to get rid of the annoying $\pm 1$. As you stated the result is that $PSL$ is the free product of the images of $S_4$ and $S_6$. This means that every element has a unique representation as a reduced word in them: i.e a word of the form $S_4^{a_1} S_6^{b_1} \dots S_4^{a_n} S_6^{b_n}$ where $a_i = 1$ and $b_i \in \{1,2\}$ and we can optionally omit the leading and/or trailing factors. From this it's easy to solve any word problem in your $a$ and $b$ (almost as easy as in a free group)
|
|
| Mar 18, 2010 at 21:44 | vote | accept | Peter Samuelson | ||
| Mar 18, 2010 at 21:07 | answer | added | Andy Putman | timeline score: 6 | |
| Mar 18, 2010 at 7:42 | history | edited | Peter Samuelson | CC BY-SA 2.5 |
added 236 characters in body
|
| Mar 18, 2010 at 7:34 | comment | added | Douglas Zare | You have to use an extra \ to get the matrices to display correctly. Similarly, to display { } use \\{ \\}. | |
| Mar 18, 2010 at 7:31 | history | edited | Douglas Zare | CC BY-SA 2.5 |
Typesetting
|
| Mar 18, 2010 at 7:26 | answer | added | Robin Chapman | timeline score: 11 | |
| Mar 18, 2010 at 7:25 | answer | added | Jack Schmidt | timeline score: 6 | |
| Mar 18, 2010 at 7:13 | history | asked | Peter Samuelson | CC BY-SA 2.5 |