Timeline for Finite index subgroup of $\mathbb{Z}^2$ that is invariant under a non-singular matrix
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 9, 2022 at 8:09 | answer | added | YCor | timeline score: 2 | |
| May 9, 2022 at 0:07 | answer | added | Johnny Calm | timeline score: 1 | |
| May 7, 2022 at 20:53 | answer | added | Will Sawin | timeline score: 3 | |
| May 7, 2022 at 19:55 | comment | added | ghc1997 | @LSpice sorry, I meant to ask "for a given $M$, which subgroups $H$ are invariant under it" | |
| May 7, 2022 at 19:43 | comment | added | LSpice | The order of the quantifiers is not clear to me. Are you asking, for a given $M$, which subspaces $H$ are stable under it or, for a given $H$, whether it is stable under some $M$? | |
| May 7, 2022 at 18:21 | comment | added | YCor | Such a subgroup contains $n\mathbf{Z}^2$. So the question "reduces" to an understanding of determining, for all $n$, invariant subgroups of $(\mathbf{Z}/n\mathbf{Z})^2$ under the reduction of $M$ modulo $n$. So the answer should be mostly of arithmetic nature. | |
| May 7, 2022 at 18:19 | history | edited | YCor | CC BY-SA 4.0 |
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| May 7, 2022 at 18:00 | history | asked | ghc1997 | CC BY-SA 4.0 |