Question

If $\rho:(\mathbb{C}^{\times})^n \rightarrow GL_m(\mathbb{C})$ is a faithful representation, does its image consist entirely of diagonal matrices?

score 73 · Answer 1 · 2019-06-20 20:06:08

73

Views

If $\rho:(\mathbb{C}^{\times})^n \rightarrow GL_m(\mathbb{C})$ is a faithful representation, does its image consist entirely of diagonal matrices?

Published on 20 Jun 2019 - 20:06

score 843 · Answer 2 · 2019-06-21 20:51:27

843

Views

What is the fibered coproduct of abelian groups?

Published on 21 Jun 2019 - 20:51

score 96 · Answer 3 · 2019-06-22 18:37:24

96

Views

If $A\oplus B\approx A$ then $B=0$?

Published on 22 Jun 2019 - 18:37

score 89 · Answer 4 · 2019-06-22 20:08:06

89

Views

How to show $\mathrm{Hom}_\mathsf{Ab}(\mathbb Z/a\mathbb Z,\mathbb Z/b\mathbb Z) \cong \mathbb Z/(a,b)\mathbb Z$?

Published on 22 Jun 2019 - 20:08

score 262 · Answer 5 · 2019-06-24 13:06:34

262

Views

For subgroups $H,K$ of $G$ if $HK$ is always a subgroup, is $G$ abelian?

Published on 24 Jun 2019 - 13:06

score 187 · Answer 6 · 2026-03-26 00:58:19

187

Views

Surjective implies injective in this case?

Published on 26 Mar 2026 - 0:58

score 98 · Answer 7 · 2026-03-26 01:03:36

98

Views

What can we say about the homomorphism restricted to this subgroup?

Published on 26 Mar 2026 - 1:03

score 231 · Answer 8 · 2019-06-30 15:50:50

231

Views

Finite abelian group whose automorphism group is some general linear group

Published on 30 Jun 2019 - 15:50

score 104 · Answer 9 · 2026-03-26 04:33:16

104

Views

On the direct product of abelian groups

Published on 26 Mar 2026 - 4:33

score 120 · Answer 10 · 2026-03-26 06:21:08

120

Views

What is the name for this generalization of dihedral groups?

Published on 26 Mar 2026 - 6:21

score 42 · Answer 11 · 2026-03-27 03:59:01

42

Views

Abelian Hitchin's equations

Published on 27 Mar 2026 - 3:59

score 67 · Answer 12 · 2019-07-02 20:09:53

67

Views

Prime Avoidance Lemma for abelian groups?

Published on 02 Jul 2019 - 20:09

score 70 · Answer 13 · 2026-03-26 02:55:13

70

Views

Under these conditions, is $f$ an isomorphism?

Published on 26 Mar 2026 - 2:55

score 84 · Answer 14 · 2026-03-25 01:15:29

84

Views

K-theory functoriality understanding

Published on 25 Mar 2026 - 1:15

score 948 · Answer 15 · 2026-03-26 04:53:50

948

Views

Show that a finite abelian group is cyclic if and only if every Sylow-p-subgroups are cyclic.

Published on 26 Mar 2026 - 4:53

List Question

If $\rho:(\mathbb{C}^{\times})^n \rightarrow GL_m(\mathbb{C})$ is a faithful representation, does its image consist entirely of diagonal matrices?

What is the fibered coproduct of abelian groups?

If $A\oplus B\approx A$ then $B=0$?

How to show $\mathrm{Hom}_\mathsf{Ab}(\mathbb Z/a\mathbb Z,\mathbb Z/b\mathbb Z) \cong \mathbb Z/(a,b)\mathbb Z$?

For subgroups $H,K$ of $G$ if $HK$ is always a subgroup, is $G$ abelian?

Surjective implies injective in this case?

What can we say about the homomorphism restricted to this subgroup?

Finite abelian group whose automorphism group is some general linear group

On the direct product of abelian groups

What is the name for this generalization of dihedral groups?

Abelian Hitchin's equations

Prime Avoidance Lemma for abelian groups?

Under these conditions, is $f$ an isomorphism?

K-theory functoriality understanding

Show that a finite abelian group is cyclic if and only if every Sylow-p-subgroups are cyclic.

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