Timeline for Under what conditions there is a one-to-one mapping between a product of matrices and the sequence of matrices leading to the product? [closed]
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13 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Jan 28, 2015 at 19:37 | history | closed |
HJRW Stefan Kohl♦ Ryan Budney Willie Wong Yemon Choi |
Needs details or clarity | |
| Jan 27, 2015 at 19:33 | review | Close votes | |||
| Jan 28, 2015 at 19:37 | |||||
| Jan 27, 2015 at 19:14 | comment | added | HJRW | Also, this question remains open largely because, although plenty of good suggestions have been made, the OP denies that they are relevant (though they clearly are). I'm therefore voting to close. | |
| Jan 27, 2015 at 19:09 | comment | added | HJRW | @TobiasFritz, it's possible that the problem of deciding whether a given matrix group is free may also be undecidable. In fact, I think this is an open question. | |
| Oct 29, 2014 at 20:38 | comment | added | Tobias Fritz | The answer strongly depends on whether your matrices are invertible or not. If they are, then the question is equivalent to asking whether the group they generate is free, and techniques like the ping-pong lemma should apply. If they are not all invertible, then you are asking whether the monoid that they generate is free, which is a more difficult problem and undecidable even for 3x3-matrices with integer coefficients, see this paper and references therein: arxiv.org/abs/0808.3112 This implies that there cannot exist any simple necessary and sufficient conditions. | |
| Jul 1, 2014 at 19:32 | comment | added | Misha | You just need ping pong for free product of several (n) infinite cyclic groups. Wikipedia is a good place to start learning about it. | |
| Jul 1, 2014 at 17:42 | comment | added | kloop | @Misha I looked at the Ping-Pong theorem on Wikipedia, and am I right in thinking that it is presented more generally there than in de la Harpe's book? It might be the case that Wikipedia's version could be used somehow for my cause. I will get back with other questions if I have any. thanks for the pointer. | |
| Jul 1, 2014 at 16:22 | comment | added | Misha | I do not understand the question: It seems you find the statement of ping-pong lemma "too simple" and at the same time is asking for help using it. | |
| Jul 1, 2014 at 15:09 | answer | added | user53000 | timeline score: -1 | |
| Jul 1, 2014 at 14:54 | comment | added | Jeremy Rouse | Wikipedia has a statement of the Ping-Pong lemma for several subgroups. | |
| Jul 1, 2014 at 14:22 | review | First posts | |||
| Jul 1, 2014 at 14:55 | |||||
| Jul 1, 2014 at 14:06 | history | asked | kloop | CC BY-SA 3.0 |