Timeline for Normalizers of the principal congruence subgroups in $\mathrm{GL}(n,\mathbf Q)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 3 at 16:38 | history | edited | Will Sawin | CC BY-SA 4.0 |
added 2 characters in body
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| Dec 3 at 13:58 | vote | accept | P.H. | ||
| Dec 3 at 13:51 | comment | added | P.H. | YCor: so any matrix $A \in \mathrm{GL}_n(\mathbf Q)$ which normalizes a principal congruence subgroup normalizes all of them. I wonder now can the problem be attacked from a different angle: knowing that $A$ normalizes $\Gamma_n(m),$ prove that $A$ normalizes $\Gamma_n(q)$ satisfying $\mathrm{gcd}(m,q)=1?$ Then the result will (also) follow from the description of the centralizer of $\mathrm{GL}_n(\mathbf Z)$ in $\mathrm{GL}_n(\mathbf Q).$ | |
| Dec 3 at 13:33 | comment | added | P.H. | YCor: thank you very much indeed. Can't upvote due to lack of points. | |
| Dec 3 at 13:16 | history | answered | YCor | CC BY-SA 4.0 |