Question

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

score 177 · Answer 1 · 2018-06-10 20:12:20

177

Views

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

Published on 10 Jun 2018 - 20:12

score 261 · Answer 2 · 2018-06-11 19:08:37

261

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 11 Jun 2018 - 19:08

score 736 · Answer 3 · 2018-06-13 13:28:44

736

Views

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

Published on 13 Jun 2018 - 13:28

score 80 · Answer 4 · 2018-06-14 14:43:37

80

Views

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

Published on 14 Jun 2018 - 14:43

score 1.9k · Answer 5 · 2026-03-25 12:16:30

1.9k

Views

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

Published on 25 Mar 2026 - 12:16

score 23 · Answer 6 · 2018-06-19 11:45:10

23

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 19 Jun 2018 - 11:45

score 70 · Answer 7 · 2018-06-21 13:07:04

70

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 21 Jun 2018 - 13:07

score 60 · Answer 8 · 2018-07-04 00:09:57

60

Views

Order of element of $A_5$

Published on 04 Jul 2018 - 0:09

score 69 · Answer 9 · 2018-07-04 13:17:16

69

Views

Find existence of surjective homomorphism throug epimorphism onto each coset

Published on 04 Jul 2018 - 13:17

score 885 · Answer 10 · 2018-07-05 13:57:02

885

Views

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

Published on 05 Jul 2018 - 13:57

score 1k · Answer 11 · 2018-07-05 20:58:12

1k

Views

Show function is an isomorphism

Published on 05 Jul 2018 - 20:58

score 91 · Answer 12 · 2018-07-05 21:24:20

91

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 05 Jul 2018 - 21:24

score 70 · Answer 13 · 2018-07-08 16:06:45

70

Views

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

Published on 08 Jul 2018 - 16:06

score 346 · Answer 14 · 2018-07-11 12:30:30

346

Views

Understanding Homomorphism counting

Published on 11 Jul 2018 - 12:30

score 53 · Answer 15 · 2018-07-13 19:07:26

53

Views

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

Published on 13 Jul 2018 - 19:07

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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