Question

Finding homomorphisms $f: \mathbb{Z}_{12} \to \mathbb{Z}_{18}$ with image of size $3$

score 3.2k · Answer 1 · 2016-11-11 22:42:51

3.2k

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Finding homomorphisms $f: \mathbb{Z}_{12} \to \mathbb{Z}_{18}$ with image of size $3$

Published on 11 Nov 2016 - 22:42

score 523 · Answer 2 · 2016-11-11 23:19:33

523

Views

There is no surjective homomorphism from $S_4$ to $D_4$.

Published on 11 Nov 2016 - 23:19

score 831 · Answer 3 · 2026-03-26 01:12:43

831

Views

Show that there exists a ring homomorphism $f: Z/(m)\rightarrow Z/(n)$ sending 1 to 1 if and only if $n|m$.

Published on 26 Mar 2026 - 1:12

score 478 · Answer 4 · 2016-11-12 17:06:31

478

Views

Finding all groups $H$ (up to isomorphism) such that there is a surjective homomorphism from $D_8$ to $H$

Published on 12 Nov 2016 - 17:06

score 82 · Answer 5 · 2026-03-28 18:14:06

82

Views

Can Paillier Homomorphic Encryption handle more than one binary plaintext?

Published on 28 Mar 2026 - 18:14

score 460 · Answer 6 · 2016-11-12 19:37:46

460

Views

How many homomorphisms quaternion group $Q_{8} \rightarrow \{\pm 1 \}$?

Published on 12 Nov 2016 - 19:37

score 186 · Answer 7 · 2016-11-14 02:22:47

186

Views

Group Homomorphisms for General Linear Groups

Published on 14 Nov 2016 - 2:22

score 157 · Answer 8 · 2016-11-14 06:46:36

157

Views

Group of order $2p$ has homomorphism onto a group of order 2

Published on 14 Nov 2016 - 6:46

score 47 · Answer 9 · 2026-03-26 19:20:00

47

Views

For finite collection of groups, $G_{1},G_{2},\dots, G_{n}$, $\exists G$ such that $G_{i}$ is a homomorphic image of $G$

Published on 26 Mar 2026 - 19:20

score 1.9k · Answer 10 · 2016-11-16 08:03:26

1.9k

Views

Show that there exists a unique homomorphism $f: \mathbb{Z} \to G$ such that $f(1)=a$

Published on 16 Nov 2016 - 8:03

score 68 · Answer 11 · 2016-11-17 00:11:55

68

Views

Let $h:S_4 \rightarrow \mathbb{Z}$ be a group homomorphism. Prove that $h(x) =0$ for all $x \in S_4$

Published on 17 Nov 2016 - 0:11

score 55 · Answer 12 · 2016-11-23 21:35:21

55

Views

Is the map $Z\times Z \to S_3$ a homomorphism?

Published on 23 Nov 2016 - 21:35

score 55 · Answer 13 · 2016-11-24 00:00:48

55

Views

Sending identities to identities while defining homomorphisms

Published on 24 Nov 2016 - 0:00

score 420 · Answer 14 · 2016-11-28 10:27:43

420

Views

How many homomorphisms are there from $\mathbb{Z}_{30}$ onto $\mathbb{Z}_{12}$?

Published on 28 Nov 2016 - 10:27

score 152 · Answer 15 · 2016-11-28 23:01:51

152

Views

Existence of nontrivial homomorphism from $Z_3$ to $\text{Aut}(Z_5 \times Z_5)$

Published on 28 Nov 2016 - 23:01

List Question

Finding homomorphisms $f: \mathbb{Z}_{12} \to \mathbb{Z}_{18}$ with image of size $3$

There is no surjective homomorphism from $S_4$ to $D_4$.

Show that there exists a ring homomorphism $f: Z/(m)\rightarrow Z/(n)$ sending 1 to 1 if and only if $n|m$.

Finding all groups $H$ (up to isomorphism) such that there is a surjective homomorphism from $D_8$ to $H$

Can Paillier Homomorphic Encryption handle more than one binary plaintext?

How many homomorphisms quaternion group $Q_{8} \rightarrow \{\pm 1 \}$?

Group Homomorphisms for General Linear Groups

Group of order $2p$ has homomorphism onto a group of order 2

For finite collection of groups, $G_{1},G_{2},\dots, G_{n}$, $\exists G$ such that $G_{i}$ is a homomorphic image of $G$

Show that there exists a unique homomorphism $f: \mathbb{Z} \to G$ such that $f(1)=a$

Let $h:S_4 \rightarrow \mathbb{Z}$ be a group homomorphism. Prove that $h(x) =0$ for all $x \in S_4$

Is the map $Z\times Z \to S_3$ a homomorphism?

Sending identities to identities while defining homomorphisms

How many homomorphisms are there from $\mathbb{Z}_{30}$ onto $\mathbb{Z}_{12}$?

Existence of nontrivial homomorphism from $Z_3$ to $\text{Aut}(Z_5 \times Z_5)$

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