Question

Find the Number of Group Homomorphisms from $\mathbb{Z}/10\mathbb{Z}$ to $A_4$.

score 155 · Answer 1 · 2020-12-15 06:11:40

155

Views

Find the Number of Group Homomorphisms from $\mathbb{Z}/10\mathbb{Z}$ to $A_4$.

Published on 15 Dec 2020 - 6:11

score 34 · Answer 2 · 2026-03-26 02:54:28

34

Views

Homomorphisms between $\mathbb{Z} \star \mathbb{Z} $ and $\mathbb{Z} _2 $

Published on 26 Mar 2026 - 2:54

score 263 · Answer 3 · 2026-03-31 17:05:22

263

Views

Find non trivial homomorphism $\mathbb{Z}/q\mathbb{Z} \rightarrow \text{Aut}(\mathbb{Z}/p\mathbb{Z})$

Published on 31 Mar 2026 - 17:05

score 71 · Answer 4 · 2026-03-31 17:02:30

71

Views

Non trivial homomorphisms $\mathbb{Z}/3\mathbb{Z} \rightarrow \text{Aut}(\mathbb{Z}/7\mathbb{Z})$

Published on 31 Mar 2026 - 17:02

score 70 · Answer 5 · 2020-12-16 13:32:38

70

Views

Let $H\lhd G$ and $\psi:G\to G/H,x\mapsto xH$ be a function. Show it is surjective

Published on 16 Dec 2020 - 13:32

score 56 · Answer 6 · 2020-12-20 15:43:02

56

Views

Showing that my function is a surjective homomorphism from $A_4$ to $\mathbb{Z}/3\mathbb{Z}$

Published on 20 Dec 2020 - 15:43

score 101 · Answer 7 · 2020-12-26 18:54:39

101

Views

Endomorphisms and K-Vector spaces

Published on 26 Dec 2020 - 18:54

score 542 · Answer 8 · 2020-12-28 14:03:14

542

Views

Show that $\mathbb{Z}/5\mathbb{Z} = \langle a\rangle$

Published on 28 Dec 2020 - 14:03

score 262 · Answer 9 · 2020-12-28 15:08:45

262

Views

Let $G$ be a group. What is ${\rm Hom}(\mathbb{Z}_n \times \mathbb{Z}_m, G)$?

Published on 28 Dec 2020 - 15:08

score 494 · Answer 10 · 2020-12-28 19:02:02

494

Views

$(f + g)_* = f_* + g_*$

Published on 28 Dec 2020 - 19:02

score 66 · Answer 11 · 2020-12-30 10:13:47

66

Views

Find homomorphism where $\ker(\phi) \cong \mathbb{Z}^3$

Published on 30 Dec 2020 - 10:13

score 186 · Answer 12 · 2020-12-31 17:28:29

186

Views

Let $\phi$ a homomorphism from $G$ to $H$. Let $K \leq G$ contain the kernel of $\phi$. Show that $\phi ^{-1}\left( \phi\left( K \right) \right) = K.$

Published on 31 Dec 2020 - 17:28

score 132 · Answer 13 · 2021-01-02 22:39:30

132

Views

Suppose that $\varphi$ is a homomorphism from $\mathbb{Z}_{36}$ to a group of order $24$. Determine the possible homomorphic images

Published on 02 Jan 2021 - 22:39

score 49 · Answer 14 · 2021-01-03 14:51:11

49

Views

Find kernel of $([x+y]_2, 2x-y)$

Published on 03 Jan 2021 - 14:51

score 110 · Answer 15 · 2021-01-03 22:15:39

110

Views

Show that $|\phi(a)| \mid|G|$

Published on 03 Jan 2021 - 22:15

List Question

Find the Number of Group Homomorphisms from $\mathbb{Z}/10\mathbb{Z}$ to $A_4$.

Homomorphisms between $\mathbb{Z} \star \mathbb{Z} $ and $\mathbb{Z} _2 $

Find non trivial homomorphism $\mathbb{Z}/q\mathbb{Z} \rightarrow \text{Aut}(\mathbb{Z}/p\mathbb{Z})$

Non trivial homomorphisms $\mathbb{Z}/3\mathbb{Z} \rightarrow \text{Aut}(\mathbb{Z}/7\mathbb{Z})$

Let $H\lhd G$ and $\psi:G\to G/H,x\mapsto xH$ be a function. Show it is surjective

Showing that my function is a surjective homomorphism from $A_4$ to $\mathbb{Z}/3\mathbb{Z}$

Endomorphisms and K-Vector spaces

Show that $\mathbb{Z}/5\mathbb{Z} = \langle a\rangle$

Let $G$ be a group. What is ${\rm Hom}(\mathbb{Z}_n \times \mathbb{Z}_m, G)$?

$(f + g)_* = f_* + g_*$

Find homomorphism where $\ker(\phi) \cong \mathbb{Z}^3$

Let $\phi$ a homomorphism from $G$ to $H$. Let $K \leq G$ contain the kernel of $\phi$. Show that $\phi ^{-1}\left( \phi\left( K \right) \right) = K.$

Suppose that $\varphi$ is a homomorphism from $\mathbb{Z}_{36}$ to a group of order $24$. Determine the possible homomorphic images

Find kernel of $([x+y]_2, 2x-y)$

Show that $|\phi(a)| \mid|G|$

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