Question

The Derivative as a group homomorphism

score 144 · Answer 1 · 2026-03-28 15:55:55

144

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The Derivative as a group homomorphism

Published on 28 Mar 2026 - 15:55

score 552 · Answer 2 · 2021-02-16 06:42:15

552

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If $H\le G$, there is a homomorphism $\phi:G\to A(H\backslash G)$ and $\ker\phi$ is the largest normal subgroup of $G$ contained in $H$

Published on 16 Feb 2021 - 6:42

score 148 · Answer 3 · 2021-02-17 18:44:37

148

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Let $f: G_{1} \rightarrow G_{2}$ be a homomorphism. Show that if $H_{1} \leq G_{1}$, then $f\left(H_{1}\right) \leq G_{2}$

Published on 17 Feb 2021 - 18:44

score 47 · Answer 4 · 2026-03-28 15:55:53

47

Views

Identifying a certain quotient with a familiar group

Published on 28 Mar 2026 - 15:55

score 67 · Answer 5 · 2021-02-19 15:33:27

67

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Smallest Image of an endomorphism?

Published on 19 Feb 2021 - 15:33

score 349 · Answer 6 · 2026-03-31 20:04:36

349

Views

Proof that group homomorphisms are associative

Published on 31 Mar 2026 - 20:04

score 428 · Answer 7 · 2021-02-19 18:33:18

428

Views

the kernel of surjective homomorphism between topological groups is closed

Published on 19 Feb 2021 - 18:33

score 88 · Answer 8 · 2021-02-19 20:41:18

88

Views

Given two adjoint functors $F$ and $G$, is the bijection ${\rm Hom}_{\mathcal A}(X,G(Y)) \cong {\rm Hom}_{\mathcal B}(F(X),Y)$ a group homomorphism?

Published on 19 Feb 2021 - 20:41

score 292 · Answer 9 · 2021-02-21 10:08:02

292

Views

How can I show that this function is a homomorphism?

Published on 21 Feb 2021 - 10:08

score 170 · Answer 10 · 2026-03-28 23:59:59

170

Views

Let $G$ be a finite group and let $x$ and $y$ be distinct elements of order 2 in $G$ that generate $G$. Prove that $G\cong D_{2n}$, where $n=|xy|.$

Published on 28 Mar 2026 - 23:59

score 91 · Answer 11 · 2021-02-28 09:00:46

91

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Why $\gcd(12,30)$ equals the number of homomorphisms from $\Bbb Z_{12}$ to $\Bbb Z_{30}$?

Published on 28 Feb 2021 - 9:00

score 99 · Answer 12 · 2021-03-03 22:36:01

99

Views

Action of the symmetry group of a cube on opposite faces defines a surjective homomorphism from $S_{4}$ to $S_{3}$

Published on 03 Mar 2021 - 22:36

score 345 · Answer 13 · 2026-04-01 05:47:18

345

Views

How to prove the action of the symmetry group of a cube on its pairs of opposite faces defines a surjective homomorphism from $S_4$ to $S_3$?

Published on 01 Apr 2026 - 5:47

score 536 · Answer 14 · 2021-03-07 08:25:33

536

Views

Prove the two preimage sets have the same size under a surjective group homomorphism (for a finite group)

Published on 07 Mar 2021 - 8:25

score 162 · Answer 15 · 2026-03-28 14:05:40

162

Views

Quotient then abelianize versus abelianize then quotient

Published on 28 Mar 2026 - 14:05

List Question

The Derivative as a group homomorphism

If $H\le G$, there is a homomorphism $\phi:G\to A(H\backslash G)$ and $\ker\phi$ is the largest normal subgroup of $G$ contained in $H$

Let $f: G_{1} \rightarrow G_{2}$ be a homomorphism. Show that if $H_{1} \leq G_{1}$, then $f\left(H_{1}\right) \leq G_{2}$

Identifying a certain quotient with a familiar group

Smallest Image of an endomorphism?

Proof that group homomorphisms are associative

the kernel of surjective homomorphism between topological groups is closed

Given two adjoint functors $F$ and $G$, is the bijection ${\rm Hom}_{\mathcal A}(X,G(Y)) \cong {\rm Hom}_{\mathcal B}(F(X),Y)$ a group homomorphism?

How can I show that this function is a homomorphism?

Let $G$ be a finite group and let $x$ and $y$ be distinct elements of order 2 in $G$ that generate $G$. Prove that $G\cong D_{2n}$, where $n=|xy|.$

Why $\gcd(12,30)$ equals the number of homomorphisms from $\Bbb Z_{12}$ to $\Bbb Z_{30}$?

Action of the symmetry group of a cube on opposite faces defines a surjective homomorphism from $S_{4}$ to $S_{3}$

How to prove the action of the symmetry group of a cube on its pairs of opposite faces defines a surjective homomorphism from $S_4$ to $S_3$?

Prove the two preimage sets have the same size under a surjective group homomorphism (for a finite group)

Quotient then abelianize versus abelianize then quotient

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