Question

Showing that a map $\mathrm{GL}(2,k) \to \mathrm{Gal}(k(x)/k)$ is a group homomorphism

score 180 · Answer 1 · 2026-04-16 02:18:20

180

Views

Showing that a map $\mathrm{GL}(2,k) \to \mathrm{Gal}(k(x)/k)$ is a group homomorphism

Published on 16 Apr 2026 - 2:18

score 263 · Answer 2 · 2026-04-16 05:30:10

263

Views

Prove if $G$ is an abelian group, then $q(x) = x^2$ defines a homomorphism from $G$ into $G$. Is $q$ ever an isomorphism?

Published on 16 Apr 2026 - 5:30

score 739 · Answer 3 · 2026-04-16 18:55:52

739

Views

Example of a homomorphism of $G$ onto $G$ that isn't $1-1$?

Published on 16 Apr 2026 - 18:55

score 83 · Answer 4 · 2026-05-10 18:44:36

83

Views

Find a homomorphism $f$ such that $\ker f = N$, a normal subgroup.

Published on 10 May 2026 - 18:44

score 1.9k · Answer 5 · 2026-05-10 20:52:34

1.9k

Views

Does there exist non trivial group homomorphism from $S_3$ to ( $\mathbb Q $,+)

Published on 10 May 2026 - 20:52

score 28 · Answer 6 · 2026-04-17 10:29:48

28

Views

Show that the function $f: ((\mathbb{Z}, +) \rightarrow (\mathbb{C}, *)$ is a homomorphism of groups with $f(x) = i^x, \forall x \in \mathbb{Z}$.

Published on 17 Apr 2026 - 10:29

score 73 · Answer 7 · 2026-04-11 15:19:59

73

Views

If $\mathbb Z^m\twoheadrightarrow\left(\mathbb Z\big /2\mathbb Z\right)^n$ is a surjective homomorphism, why is then $m=n$?

Published on 11 Apr 2026 - 15:19

score 63 · Answer 8 · 2026-04-12 08:21:05

63

Views

Order of element of $A_5$

Published on 12 Apr 2026 - 8:21

score 72 · Answer 9 · 2026-04-15 13:29:31

72

Views

Find existence of surjective homomorphism throug epimorphism onto each coset

Published on 15 Apr 2026 - 13:29

score 888 · Answer 10 · 2026-04-11 02:46:09

888

Views

Is it possible to check injectivity of a homomorphism by checking just the generators of the group?

Published on 11 Apr 2026 - 2:46

score 1k · Answer 11 · 2026-04-10 17:56:07

1k

Views

Show function is an isomorphism

Published on 10 Apr 2026 - 17:56

score 94 · Answer 12 · 2026-04-15 05:34:39

94

Views

Given $(G,*)$ a group. Show the function $f: G \to G$ defined as $f(a)=a^{2}$ is an homomorphism if and only if G is abelian.

Published on 15 Apr 2026 - 5:34

score 73 · Answer 13 · 2026-04-10 19:08:11

73

Views

Is it always possible to take $H$ such that $\phi_1$ is injective?

Published on 10 Apr 2026 - 19:08

score 349 · Answer 14 · 2026-04-08 21:25:24

349

Views

Understanding Homomorphism counting

Published on 08 Apr 2026 - 21:25

score 56 · Answer 15 · 2026-04-15 20:17:51

56

Views

The image of a homomorphism on the group of $F_p$-rational points on an elliptic curve

Published on 15 Apr 2026 - 20:17

List Question

Showing that a map $\mathrm{GL}(2,k) \to \mathrm{Gal}(k(x)/k)$ is a group homomorphism

Prove if $G$ is an abelian group, then $q(x) = x^2$ defines a homomorphism from $G$ into $G$. Is $q$ ever an isomorphism?

Example of a homomorphism of $G$ onto $G$ that isn't $1-1$?

Find a homomorphism $f$ such that $\ker f = N$, a normal subgroup.

Does there exist non trivial group homomorphism from $S_3$ to ( $\mathbb Q $,+)

Show that the function $f: ((\mathbb{Z}, +) \rightarrow (\mathbb{C}, *)$ is a homomorphism of groups with $f(x) = i^x, \forall x \in \mathbb{Z}$.

If $\mathbb Z^m\twoheadrightarrow\left(\mathbb Z\big /2\mathbb Z\right)^n$ is a surjective homomorphism, why is then $m=n$?

Order of element of $A_5$

Find existence of surjective homomorphism throug epimorphism onto each coset

Is it possible to check injectivity of a homomorphism by checking just the generators of the group?

Show function is an isomorphism

Given $(G,*)$ a group. Show the function $f: G \to G$ defined as $f(a)=a^{2}$ is an homomorphism if and only if G is abelian.

Is it always possible to take $H$ such that $\phi_1$ is injective?

Understanding Homomorphism counting

The image of a homomorphism on the group of $F_p$-rational points on an elliptic curve

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