User GreginGre

7 votes

0 answers

441 views

Which groups can be proven to be simple using Iwasawa criterion?

asked Sep 21, 2019 at 7:36

7 votes

4 answers

700 views

When does a finite group $G$ have an element of order equal to its exponent?

asked Nov 5, 2021 at 9:11

6 votes

1 answer

136 views

Generic $Q_8$-polynomial in characteristic $2$

asked Feb 13, 2023 at 13:38

6 votes

0 answers

73 views

Hilbert 90 for cyclic Galois ring extension

asked Apr 4, 2023 at 17:41

6 votes

1 answer

83 views

What is the order of the following subgroup $\langle (1 \ 2 \ \cdots \ n), (a \ b)\rangle$ of $S_n$?

asked Mar 17 at 13:36

5 votes

0 answers

112 views

Does an algebra automorphism of $M_n(R)$ preserves the characteristic polynomial?

asked Apr 6, 2023 at 14:12

5 votes

1 answer

124 views

$\bigcap\limits_{\varphi\in E^*}\ker(\varphi)$ and the Axiom of Choise

asked May 31, 2023 at 14:03

5 votes

0 answers

296 views

Cute/striking application(s) of Snake Lemma outside homological algebra

asked Jun 7, 2019 at 12:52

4 votes

0 answers

263 views

Nice (and rather short) applications of module theory for a book chapter

asked Oct 7, 2019 at 14:09

4 votes

0 answers

132 views

Finite groups $G$ such that every Galois extension of group $G$ is totally real

asked Jan 28, 2022 at 17:38

4 votes

1 answer

94 views

$R$-modules satisfying $M^{\otimes n}\simeq R$ but not $M^n\simeq R^n$

asked May 4, 2023 at 15:19

3 votes

0 answers

57 views

Counterexample to Noether's problem not using heavy machinery

asked Aug 6, 2022 at 15:34

3 votes

0 answers

54 views

Structure of the subgroup of $S_n$ generated by a $n$-cycle and a transposition

asked Mar 19 at 18:06

3 votes

1 answer

71 views

Is $GL_n(\mathbb{F}_2)$ generated by a Jordan cell of size $n$ and its transpose?

asked Jan 26, 2022 at 6:38

3 votes

0 answers

81 views

Automorphisms of matrix algebras and Picard Group

asked May 4, 2023 at 15:04

3 votes

1 answer

137 views

Polynomials for which the induced polynomial map is zero

asked Sep 17, 2020 at 16:56

3 votes

0 answers

49 views

$G$ $p$-group, $G^{ab}\simeq \mathbb{Z}/p\mathbb{Z}$ implies $G\simeq \mathbb{Z}/p\mathbb{Z}$

asked Oct 26, 2017 at 21:55

2 votes

0 answers

48 views

Torsors over separable closure

asked Apr 9, 2018 at 8:54

2 votes

1 answer

76 views

Ring of integers of arithmetically disjoint fields

asked Jul 5, 2019 at 19:27

2 votes

1 answer

905 views

Does a prime ideal contains an irreducible element?

asked Jun 9, 2020 at 13:48

2 votes

0 answers

124 views

Ad hoc proof of Minkowski's bound for $\mathbb{Q}(\sqrt{-19})$

asked Sep 10, 2020 at 17:18

2 votes

0 answers

53 views

Is $\mathbb{Z}/n\mathbb{Z}[X]/(f)$ a principal ideal ring?

asked Sep 17, 2020 at 13:10

2 votes

0 answers

40 views

Cardinality of $\operatorname{Hom}_{K\text{-alg}}(A,L),$ where $A$ is a finite dim. $K$-alg, $L/K$ a field extension

asked Jan 1, 2020 at 15:19

2 votes

0 answers

58 views

Non irreducible characters with real values

asked Jun 30, 2023 at 12:48

2 votes

0 answers

39 views

Number of conjugacy classes of integral matrices with irreducible characteristic polynomials and ideal classes

asked Sep 15, 2023 at 18:29

2 votes

1 answer

61 views

Is the inverse of a finitely generated $A$-submodule of $\mathrm{Frac}(A)$ still finitely generated?

asked Oct 12, 2023 at 16:37

2 votes

0 answers

36 views

Ad hoc proof of the fact that the localization of a ring of integers at a nonzero prime ideal is a PID

asked Oct 13, 2023 at 16:26

2 votes

1 answer

63 views

Is $F^\times/N_{L/F}(L^\times)$ non trivial or infinite when $L/F$ is an extension of global fields?

asked Jan 28, 2022 at 18:02

2 votes

1 answer

49 views

Is $K^\times/F^\times N_{L/K}(L^\times)$ infinite when $L/F$ is a biquadratic extension of a number field $F$?

asked Aug 21 at 19:13

2 votes

1 answer

102 views

If $\vert d\vert\geq 3$, is $-1+\sqrt{d}$ an irreducible element of $\mathbb{Z}[\sqrt{d}]$?

asked Feb 12 at 11:56

Stack Exchange Network

46 Questions

Which groups can be proven to be simple using Iwasawa criterion?

When does a finite group $G$ have an element of order equal to its exponent?

Generic $Q_8$-polynomial in characteristic $2$

Hilbert 90 for cyclic Galois ring extension

What is the order of the following subgroup $\langle (1 \ 2 \ \cdots \ n), (a \ b)\rangle$ of $S_n$?

Does an algebra automorphism of $M_n(R)$ preserves the characteristic polynomial?

$\bigcap\limits_{\varphi\in E^*}\ker(\varphi)$ and the Axiom of Choise

Cute/striking application(s) of Snake Lemma outside homological algebra

Nice (and rather short) applications of module theory for a book chapter

Finite groups $G$ such that every Galois extension of group $G$ is totally real

$R$-modules satisfying $M^{\otimes n}\simeq R$ but not $M^n\simeq R^n$

Counterexample to Noether's problem not using heavy machinery

Structure of the subgroup of $S_n$ generated by a $n$-cycle and a transposition

Is $GL_n(\mathbb{F}_2)$ generated by a Jordan cell of size $n$ and its transpose?

Automorphisms of matrix algebras and Picard Group

Polynomials for which the induced polynomial map is zero

$G$ $p$-group, $G^{ab}\simeq \mathbb{Z}/p\mathbb{Z}$ implies $G\simeq \mathbb{Z}/p\mathbb{Z}$

Torsors over separable closure

Ring of integers of arithmetically disjoint fields

Does a prime ideal contains an irreducible element?

Ad hoc proof of Minkowski's bound for $\mathbb{Q}(\sqrt{-19})$

Is $\mathbb{Z}/n\mathbb{Z}[X]/(f)$ a principal ideal ring?

Cardinality of $\operatorname{Hom}_{K\text{-alg}}(A,L),$ where $A$ is a finite dim. $K$-alg, $L/K$ a field extension

Non irreducible characters with real values

Number of conjugacy classes of integral matrices with irreducible characteristic polynomials and ideal classes

Is the inverse of a finitely generated $A$-submodule of $\mathrm{Frac}(A)$ still finitely generated?

Ad hoc proof of the fact that the localization of a ring of integers at a nonzero prime ideal is a PID

Is $F^\times/N_{L/F}(L^\times)$ non trivial or infinite when $L/F$ is an extension of global fields?

Is $K^\times/F^\times N_{L/K}(L^\times)$ infinite when $L/F$ is a biquadratic extension of a number field $F$?

If $\vert d\vert\geq 3$, is $-1+\sqrt{d}$ an irreducible element of $\mathbb{Z}[\sqrt{d}]$?