ag.algebraic-geometry stacks algebraic-stacks algebraic-spaces asked Sep 13, 2016 at 0:52

mathoverflow.net

23 votes

For which $n$ is it true that all surjections $SL_2(\mathbb{Z})\rightarrow SL_2(\mathbb{Z}/n\mathbb{Z})$ have kernel $\Gamma(n)$?

ag.algebraic-geometry nt.number-theory gr.group-theory asked Sep 27, 2016 at 6:32

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23 votes

Is $\widehat{\mathbb{Z}}[[t]]\cong\widehat{\mathbb{Z}}[[\widehat{\mathbb{Z}}]]$?

gr.group-theory ac.commutative-algebra ra.rings-and-algebras profinite-groups asked Feb 6, 2017 at 8:21

mathoverflow.net

17 votes

Is every normal subgroup of $\mathrm{SL}_2(\mathbb{Z}/n)$ also normal inside $\mathrm{GL}_2(\mathbb{Z}/n)$?

gr.group-theory finite-groups asked Jan 14, 2017 at 0:39

mathoverflow.net

16 votes

How should I think about the module of coinvariants of a $G$-module?

gr.group-theory rt.representation-theory ac.commutative-algebra linear-algebra asked Oct 11, 2018 at 0:02

mathoverflow.net

14 votes

When is the inverse image of the structure sheaf the structure sheaf?

ag.algebraic-geometry asked Nov 23, 2017 at 18:59

mathoverflow.net

14 votes

Invariants of matrices (by simultaneous $\mathrm{GL}_n$ conjugation) over arbitrary rings

ag.algebraic-geometry rt.representation-theory ac.commutative-algebra quivers asked Sep 6, 2021 at 23:31

mathoverflow.net

13 votes

Difference between the completed group algebra and the profinite completion of a group ring

gr.group-theory profinite-groups asked Feb 6, 2017 at 6:54

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12 votes

are the congruence subgroups $\Gamma(n)$ characteristic inside $\mathrm{SL}_2(\mathbb{Z})$?

ag.algebraic-geometry nt.number-theory gr.group-theory asked Sep 27, 2016 at 0:42

mathoverflow.net

11 votes

Are there open subgroups of $SL_2(\widehat{\mathbb{Z}})$ which are $GL_2(\widehat{\mathbb{Z}})$-conjugate, but not $SL_2$-conjugate?

nt.number-theory gr.group-theory profinite-groups asked Aug 18, 2017 at 21:24

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For which $n$ is it true that all surjections $SL_2(\mathbb{Z})\rightarrow SL_2(\mathbb{Z}/n\mathbb{Z})$ have kernel $\Gamma(n)$?

Is $\widehat{\mathbb{Z}}[[t]]\cong\widehat{\mathbb{Z}}[[\widehat{\mathbb{Z}}]]$?

Is every normal subgroup of $\mathrm{SL}_2(\mathbb{Z}/n)$ also normal inside $\mathrm{GL}_2(\mathbb{Z}/n)$?

How should I think about the module of coinvariants of a $G$-module?

When is the inverse image of the structure sheaf the structure sheaf?

Invariants of matrices (by simultaneous $\mathrm{GL}_n$ conjugation) over arbitrary rings

Difference between the completed group algebra and the profinite completion of a group ring

are the congruence subgroups $\Gamma(n)$ characteristic inside $\mathrm{SL}_2(\mathbb{Z})$?

Are there open subgroups of $SL_2(\widehat{\mathbb{Z}})$ which are $GL_2(\widehat{\mathbb{Z}})$-conjugate, but not $SL_2$-conjugate?