Timeline for A free subgroup of GL(2,Z)?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Nov 21, 2010 at 21:21 | comment | added | Sándor Kovács | Kevin, I thought that you'd know that. I didn't mean to imply anything to the contrary. It is indeed a useful trick. Thanks. :) | |
| Nov 21, 2010 at 21:18 | history | edited | Kevin Buzzard | CC BY-SA 2.5 |
question edited so answer edited to clarify.
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| Nov 21, 2010 at 21:17 | comment | added | Kevin Buzzard | @Sandor: yes I know my first para is logically superfluous---it was an attempt to answer the question "any relevant references will be appreciated". | |
| Nov 21, 2010 at 21:12 | comment | added | Sándor Kovács | Kevin, I guess the meaning is simply that the subgroup of relations (in the $F_2$ that maps onto this group) is not generated by a single element. Probably not too surprising. Also, even though the statement you mention in the first paragraph is interesting, it is not really needed here. I mean you are using the easy direction, that is, that if there is a non-trivial relation then the group is not free. | |
| Nov 21, 2010 at 20:51 | comment | added | Kevin Buzzard | I will perhaps remark that I spotted $ba^{−2}ba^{−2}=1$ and Mark spotted $[a,b]^6=1$, and these look to me like "distinct relations", if that has any meaning... | |
| Nov 21, 2010 at 20:49 | comment | added | Kevin Buzzard | OK! I don't understand the modified question, so don't expect any more from me :-) | |
| Nov 21, 2010 at 20:43 | comment | added | Nikita Sidorov | Kevin, thanks! I have modified my question. | |
| Nov 21, 2010 at 20:33 | history | answered | Kevin Buzzard | CC BY-SA 2.5 |