Question

If $G$ is simple and finite, and H subgroup then $|G|$ divides $[G:H]!/2$

score 333 · Answer 1 · 2026-03-28 11:52:03

333

Views

If $G$ is simple and finite, and H subgroup then $|G|$ divides $[G:H]!/2$

Published on 28 Mar 2026 - 11:52

score 541 · Answer 2 · 2021-01-23 18:01:52

541

Views

Homomorphisms from $\mathbb{Z}[x] \to R$

Published on 23 Jan 2021 - 18:01

score 181 · Answer 3 · 2021-01-24 22:18:34

181

Views

Show that $\alpha$ is a homomorphism. Also, find $\text{ker}(\alpha)$, and decide if $\alpha$ is onto.

Published on 24 Jan 2021 - 22:18

score 178 · Answer 4 · 2021-01-27 19:10:54

178

Views

Show that $\alpha(a) = h$ if and only if $a = gk$ for some $k \in \text{ker} (\alpha)$

Published on 27 Jan 2021 - 19:10

score 117 · Answer 5 · 2021-01-29 14:43:09

117

Views

Indicated quantities for the given group homomorphism

Published on 29 Jan 2021 - 14:43

score 141 · Answer 6 · 2021-01-30 10:55:18

141

Views

Let $G,H$ be linear lie groups. Prove that any continuous homomorphism $\Phi:G\to H$ is differentiable.

Published on 30 Jan 2021 - 10:55

score 117 · Answer 7 · 2026-03-26 01:23:41

117

Views

Is $\phi_*X\in\mathfrak{X}(H)$ left invariant if $X\in\mathfrak{X}(G)$ is left invariant and $\phi\colon G\to H$ is a Lie group homomorphism?

Published on 26 Mar 2026 - 1:23

score 177 · Answer 8 · 2021-02-01 23:04:27

177

Views

Prove that $\phi$ is injective by showing the kernel is trivial.

Published on 01 Feb 2021 - 23:04

score 65 · Answer 9 · 2026-03-31 20:25:45

65

Views

Group homomorphism between $\mathbb{Z}_2$ and ${\rm Aut}(G)$.

Published on 31 Mar 2026 - 20:25

score 41 · Answer 10 · 2021-02-04 10:25:25

41

Views

Show: $\ker(b) \cong \ker(a)/U$.

Published on 04 Feb 2021 - 10:25

score 139 · Answer 11 · 2021-02-05 12:11:29

139

Views

How to calculate number of onto and one homomorphism?

Published on 05 Feb 2021 - 12:11

score 127 · Answer 12 · 2021-02-09 18:21:54

127

Views

Every proper subgroup of $\mathbb{Z}(p^{\infty})$ is of the form $\left\langle \, \overline{\frac{1}{p^n}} \, \right\rangle$ for some $n>0$.

Published on 09 Feb 2021 - 18:21

score 313 · Answer 13 · 2021-02-12 04:24:41

313

Views

Induced homomorphism in homology is surjective for finite regular covering maps

Published on 12 Feb 2021 - 4:24

score 74 · Answer 14 · 2026-03-28 08:10:01

74

Views

Show that exists an epimorphism $\phi_i: T \rightarrow G_i$ and find $\ker(\phi_i)$

Published on 28 Mar 2026 - 8:10

score 371 · Answer 15 · 2021-02-13 21:12:48

371

Views

Basic proof that Isogeny = group homomorphism without Riemann Roch?

Published on 13 Feb 2021 - 21:12

List Question

If $G$ is simple and finite, and H subgroup then $|G|$ divides $[G:H]!/2$

Homomorphisms from $\mathbb{Z}[x] \to R$

Show that $\alpha$ is a homomorphism. Also, find $\text{ker}(\alpha)$, and decide if $\alpha$ is onto.

Show that $\alpha(a) = h$ if and only if $a = gk$ for some $k \in \text{ker} (\alpha)$

Indicated quantities for the given group homomorphism

Let $G,H$ be linear lie groups. Prove that any continuous homomorphism $\Phi:G\to H$ is differentiable.

Is $\phi_*X\in\mathfrak{X}(H)$ left invariant if $X\in\mathfrak{X}(G)$ is left invariant and $\phi\colon G\to H$ is a Lie group homomorphism?

Prove that $\phi$ is injective by showing the kernel is trivial.

Group homomorphism between $\mathbb{Z}_2$ and ${\rm Aut}(G)$.

Show: $\ker(b) \cong \ker(a)/U$.

How to calculate number of onto and one homomorphism?

Every proper subgroup of $\mathbb{Z}(p^{\infty})$ is of the form $\left\langle \, \overline{\frac{1}{p^n}} \, \right\rangle$ for some $n>0$.

Induced homomorphism in homology is surjective for finite regular covering maps

Show that exists an epimorphism $\phi_i: T \rightarrow G_i$ and find $\ker(\phi_i)$

Basic proof that Isogeny = group homomorphism without Riemann Roch?

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