Question

Let $\varphi: G \rightarrow H$ be a group homomorphism, and $a, b \in G$ such that $|a| = |b|$, is $|\varphi(a)|=|\varphi(b)|$?

score 70 · Answer 1 · 2020-10-12 12:00:09

70

Views

Let $\varphi: G \rightarrow H$ be a group homomorphism, and $a, b \in G$ such that $|a| = |b|$, is $|\varphi(a)|=|\varphi(b)|$?

Published on 12 Oct 2020 - 12:00

score 1.3k · Answer 2 · 2020-10-13 13:49:58

1.3k

Views

Show that all groups of order $3$ are isomorphic with each other.

Published on 13 Oct 2020 - 13:49

score 146 · Answer 3 · 2020-10-13 17:24:17

146

Views

Order of $\phi: g^i \mapsto g^{mi}$

Published on 13 Oct 2020 - 17:24

score 78 · Answer 4 · 2020-10-14 22:48:38

78

Views

A group homomorphism satisfying square property for certain elements

Published on 14 Oct 2020 - 22:48

score 211 · Answer 5 · 2020-10-15 05:17:35

211

Views

Is the Kernel of a homomorphism normal only when the homomorphism is into ? Why?

Published on 15 Oct 2020 - 5:17

score 116 · Answer 6 · 2020-10-17 06:48:24

116

Views

Kernel Dihedral group

Published on 17 Oct 2020 - 6:48

score 1.3k · Answer 7 · 2026-03-28 03:27:42

1.3k

Views

Quotient of a group by kernel of group homomorphism

Published on 28 Mar 2026 - 3:27

score 111 · Answer 8 · 2020-10-17 14:52:29

111

Views

Show that $\pi^{-1}(\tilde{H})$ is a subgroup of order $|\tilde{H}|\cdot |N|$ where $\tilde{H}$ is a subgroup of $G/N$

Published on 17 Oct 2020 - 14:52

score 76 · Answer 9 · 2026-03-28 03:03:04

76

Views

Show $(G\times H)/(K\times K') \cong G/K\times H/K'$ if $K\lhd G$ and $K'\lhd H$

Published on 28 Mar 2026 - 3:03

score 39 · Answer 10 · 2020-10-18 22:55:32

39

Views

Prove that the following is a homomorphism:

Published on 18 Oct 2020 - 22:55

score 400 · Answer 11 · 2026-03-25 18:46:33

400

Views

Natural transformations $Id_{Ab} \rightarrow Id_{Ab}$

Published on 25 Mar 2026 - 18:46

score 1.1k · Answer 12 · 2020-10-20 12:37:34

1.1k

Views

Is $G/H$ isomorphic to $G'$ if there exists an homomorphism between $G$ and $G'$ and $H$ being a normal subgroup?

Published on 20 Oct 2020 - 12:37

score 229 · Answer 13 · 2020-10-21 23:18:15

229

Views

bijective homomorphism between complex numbers and reals

Published on 21 Oct 2020 - 23:18

score 141 · Answer 14 · 2020-10-22 02:09:43

141

Views

Is there a nontrivial homomorphism $\mathbb{Q} \to SL_n(\mathbb{Z})$?

Published on 22 Oct 2020 - 2:09

score 54 · Answer 15 · 2020-10-22 14:47:27

54

Views

Construct representation of $G$ from representation of $G/N$

Published on 22 Oct 2020 - 14:47

List Question

Let $\varphi: G \rightarrow H$ be a group homomorphism, and $a, b \in G$ such that $|a| = |b|$, is $|\varphi(a)|=|\varphi(b)|$?

Show that all groups of order $3$ are isomorphic with each other.

Order of $\phi: g^i \mapsto g^{mi}$

A group homomorphism satisfying square property for certain elements

Is the Kernel of a homomorphism normal only when the homomorphism is into ? Why?

Kernel Dihedral group

Quotient of a group by kernel of group homomorphism

Show that $\pi^{-1}(\tilde{H})$ is a subgroup of order $|\tilde{H}|\cdot |N|$ where $\tilde{H}$ is a subgroup of $G/N$

Show $(G\times H)/(K\times K') \cong G/K\times H/K'$ if $K\lhd G$ and $K'\lhd H$

Prove that the following is a homomorphism:

Natural transformations $Id_{Ab} \rightarrow Id_{Ab}$

Is $G/H$ isomorphic to $G'$ if there exists an homomorphism between $G$ and $G'$ and $H$ being a normal subgroup?

bijective homomorphism between complex numbers and reals

Is there a nontrivial homomorphism $\mathbb{Q} \to SL_n(\mathbb{Z})$?

Construct representation of $G$ from representation of $G/N$

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