Question

Do any two nontrivial groups $G_1, G_2 $ have a nontrivial homomorphism between them?

score 76 · Answer 1 · 2017-10-20 16:26:34

76

Views

Do any two nontrivial groups $G_1, G_2 $ have a nontrivial homomorphism between them?

Published on 20 Oct 2017 - 16:26

score 354 · Answer 2 · 2017-10-21 15:03:59

354

Views

Can the pre-image (under homomorphism) of a subgroup be empty?

Published on 21 Oct 2017 - 15:03

score 499 · Answer 3 · 2026-03-28 09:53:33

499

Views

Describe all homomorphic images of the dihedral group $D_3$ of order 6

Published on 28 Mar 2026 - 9:53

score 73 · Answer 4 · 2017-10-24 04:57:06

73

Views

Why is this not a homomorphism?

Published on 24 Oct 2017 - 4:57

score 233 · Answer 5 · 2017-10-24 06:18:11

233

Views

Find all homomorphisms from $\Bbb{Z}_{45}\to\Bbb{Z}_{36}$

Published on 24 Oct 2017 - 6:18

score 386 · Answer 6 · 2017-10-25 05:02:20

386

Views

Determine the kernel of a homomorphism $θ: S_3 \rightarrow G$?

Published on 25 Oct 2017 - 5:02

score 845 · Answer 7 · 2026-04-01 11:36:28

845

Views

Is every group homomorphism the induced homomorphism of a continuous function?

Published on 01 Apr 2026 - 11:36

score 185 · Answer 8 · 2017-10-25 15:23:26

185

Views

Surjective homomorphism from $\mathbb{Z} \times \mathbb{Z}$ into $\mathbb{Z} \times (\mathbb{Z}/2\mathbb{Z})$

Published on 25 Oct 2017 - 15:23

score 142 · Answer 9 · 2017-10-26 03:44:34

142

Views

For any additive function, $f: (\mathbb{Q}, +)\to (\mathbb{Q}, +)$, why does $f(nx) = nf(x)$?

Published on 26 Oct 2017 - 3:44

score 23 · Answer 10 · 2026-04-01 11:02:23

23

Views

Why is $ f:x \mapsto bx $homomorphic?

Published on 01 Apr 2026 - 11:02

score 75 · Answer 11 · 2017-10-27 01:14:10

75

Views

Why are the rationals fixed by this monomorphism?

Published on 27 Oct 2017 - 1:14

score 317 · Answer 12 · 2017-10-29 18:02:13

317

Views

Condition for nontrivial homomorphism to exist between two groups?

Published on 29 Oct 2017 - 18:02

score 256 · Answer 13 · 2017-10-30 06:04:34

256

Views

How many homomorphism are there from the cyclic group $\mathbb{Z}_6$ to $\mathbb{Z}_2\times \mathbb{Z_4}$

Published on 30 Oct 2017 - 6:04

score 73 · Answer 14 · 2017-10-30 18:19:09

73

Views

Informal thoughts of group homomorphisms.

Published on 30 Oct 2017 - 18:19

score 240 · Answer 15 · 2017-10-31 20:34:19

240

Views

proving a property of elements under homomorphism

Published on 31 Oct 2017 - 20:34

List Question

Do any two nontrivial groups $G_1, G_2 $ have a nontrivial homomorphism between them?

Can the pre-image (under homomorphism) of a subgroup be empty?

Describe all homomorphic images of the dihedral group $D_3$ of order 6

Why is this not a homomorphism?

Find all homomorphisms from $\Bbb{Z}_{45}\to\Bbb{Z}_{36}$

Determine the kernel of a homomorphism $θ: S_3 \rightarrow G$?

Is every group homomorphism the induced homomorphism of a continuous function?

Surjective homomorphism from $\mathbb{Z} \times \mathbb{Z}$ into $\mathbb{Z} \times (\mathbb{Z}/2\mathbb{Z})$

For any additive function, $f: (\mathbb{Q}, +)\to (\mathbb{Q}, +)$, why does $f(nx) = nf(x)$?

Why is $ f:x \mapsto bx $homomorphic?

Why are the rationals fixed by this monomorphism?

Condition for nontrivial homomorphism to exist between two groups?

How many homomorphism are there from the cyclic group $\mathbb{Z}_6$ to $\mathbb{Z}_2\times \mathbb{Z_4}$

Informal thoughts of group homomorphisms.

proving a property of elements under homomorphism

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