Timeline for Generators for the semigroup $\mathrm{SL}(n,\mathbb{N})$

11 events

when toggle format	what		by	license	comment
May 7, 2019 at 22:04	vote	accept	Walter Simon
May 7, 2019 at 21:10	answer	added	Andrei Smolensky		timeline score: 3
May 7, 2019 at 16:29	comment	added	Walter Simon		I edited the question. I hope it will be more clear now.
May 7, 2019 at 16:28	history	edited	Walter Simon	CC BY-SA 4.0	added 1885 characters in body
May 7, 2019 at 15:53	comment	added	Mark Fischler		Unless somebody points out that the counterexample given by de la Salle is flawed, isn't the answer to the OP's question that the conjecture is false?
May 7, 2019 at 15:44	comment	added	Mikael de la Salle		I do not understand your comment. What do you mean by "elementary matrix that preserves $\mathrm{SL}(n,\mathbb{N})$"?
May 7, 2019 at 15:26	comment	added	Walter Simon		The idea is that the generators will be all the elementary matrices that preserve $\mathrm{SL}(n,\mathbb{N})$. For $n=2$ we don't need permutation matrices because the only even permutation of $\{1,2\}$ is the identity but, as you notice, it appears we can't avoid them for $n\geq 3$.
May 7, 2019 at 15:16	comment	added	Mikael de la Salle		What about $\begin{pmatrix} 0&1&0\\0&0&1\\ 1&0&0\end{pmatrix}$?
May 7, 2019 at 15:00	history	edited	YCor	CC BY-SA 4.0	added 69 characters in body
May 7, 2019 at 14:27	history	edited	Walter Simon	CC BY-SA 4.0	added 31 characters in body
May 7, 2019 at 14:13	history	asked	Walter Simon	CC BY-SA 4.0