For which $n$ is the "principal congruence subgroup" $\Gamma(n)\le \mathrm{SL}_2(\mathbb{Z})$, the subgroup consisting of matrices congruent to the identity modulo $n$, characteristic? I.e., for which $n$ is $\Gamma(n)$ stable (as a set) under all automorphisms of $\mathrm{SL}_2(\mathbb{Z})$?
2 of 2
"left invariant" -> "stable" (to avoid confusion with left vs. right), and then some more re-writing.
LSpice
- 12.9k
- 4
- 45
- 69
are the congruence subgroups $\Gamma(n)$ characteristic inside $\mathrm{SL}_2(\mathbb{Z})$?
stupid_question_bot
- 7.5k
- 1
- 12
- 45