Timeline for Any open subgroup of $GL_n(K)$ contains $U_n(K)$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 23, 2021 at 21:02 | comment | added | Will Sawin | I don't know a reference, but the proof is short: You can conjugate any unipotent upper triangular matrix by a diagonal matrix (with $i$th diagonal entry $p^{ni}$, say) to obtain a matrix which is congruent to $1$ modulo an arbitrarily high power of $p$, hence in an arbitrary open neighborhood of the identity. | |
| Aug 23, 2021 at 20:31 | comment | added | Bryan Shih | Thanks, is there a reference for the normal case? | |
| Aug 23, 2021 at 19:33 | comment | added | Paul Broussous | This is true if the subgroup is normal. This not true in general: e.g. take a congruence subgroup. | |
| Aug 23, 2021 at 19:25 | history | asked | Bryan Shih | CC BY-SA 4.0 |