Question

The attributes of the defined direct product.

score 34 · Answer 1 · 2026-04-14 07:41:06

34

Views

The attributes of the defined direct product.

Published on 14 Apr 2026 - 7:41

score 123 · Answer 2 · 2026-04-15 22:44:29

123

Views

For homomorphism $\phi:G\to H$, show that if $g\in G$ and $|g|=n$, then $|\phi(g)|$ divides $n$.

Published on 15 Apr 2026 - 22:44

score 75 · Answer 3 · 2026-04-16 18:06:40

75

Views

For homomorphism $\phi: G\to H$, if $G_{1}\leq G$ and $|G_{1}|=n$, then $|\phi(G_{1})|$ divides $n$.

Published on 16 Apr 2026 - 18:06

score 429 · Answer 4 · 2026-04-16 04:59:44

429

Views

Determine all group homomorphisms of the form $\phi: \mathbb{Z}_{12}\to \mathbb{Z}_{30}$.

Published on 16 Apr 2026 - 4:59

score 75 · Answer 5 · 2026-04-14 23:07:21

75

Views

Show that the following $\phi: \mathbb{R}\to GL_{2}(\mathbb{R})$ is not a homomorphism.

Published on 14 Apr 2026 - 23:07

score 182 · Answer 6 · 2026-04-15 22:06:42

182

Views

Show that $\phi: \mathbb{R^{n}}\to \mathbb{R^{m}}$ defined by $\phi(x)=Ax$ is a homomorphism.

Published on 15 Apr 2026 - 22:06

score 43 · Answer 7 · 2026-04-08 18:48:40

43

Views

$\mathbb{Z}^k/A\mathbb{Z}^k \cong\mathbb{Z}^k/A'\mathbb{Z}^k$

Published on 08 Apr 2026 - 18:48

score 43 · Answer 8 · 2026-04-09 13:14:59

43

Views

Is this definition of group homomorphism complete?

Published on 09 Apr 2026 - 13:14

score 70 · Answer 9 · 2026-04-15 19:23:58

70

Views

Show $\phi$ is a homomorphism, where $(a\star b)_i=a_i+b_{i+\sum_j^p a_j}$

Published on 15 Apr 2026 - 19:23

score 361 · Answer 10 · 2026-04-15 13:57:50

361

Views

Group Homomorphism: Is it required to have the inverse preservation to prove Identity Mappings?

Published on 15 Apr 2026 - 13:57

score 119 · Answer 11 · 2026-04-13 21:35:37

119

Views

Is the following claim correct in general?

Published on 13 Apr 2026 - 21:35

score 3.3k · Answer 12 · 2026-05-10 13:50:18

3.3k

Views

Find all homomorphisms $\phi: \Bbb{Z}/6\Bbb{Z} \to \Bbb{Z}/15\Bbb{Z}$.

Published on 10 May 2026 - 13:50

score 70 · Answer 13 · 2026-04-10 20:43:55

70

Views

Homomorphism and abelian group.

Published on 10 Apr 2026 - 20:43

score 155 · Answer 14 · 2026-04-14 05:03:35

155

Views

Homomorphism $ z \rightarrow\frac{z}{|z|}$

Published on 14 Apr 2026 - 5:03

score 57 · Answer 15 · 2026-04-12 04:15:43

57

Views

How many group homomorphisms between $\mathbb Z_{15}$ and $\mathbb Z_8$

Published on 12 Apr 2026 - 4:15

List Question

The attributes of the defined direct product.

For homomorphism $\phi:G\to H$, show that if $g\in G$ and $|g|=n$, then $|\phi(g)|$ divides $n$.

For homomorphism $\phi: G\to H$, if $G_{1}\leq G$ and $|G_{1}|=n$, then $|\phi(G_{1})|$ divides $n$.

Determine all group homomorphisms of the form $\phi: \mathbb{Z}_{12}\to \mathbb{Z}_{30}$.

Show that the following $\phi: \mathbb{R}\to GL_{2}(\mathbb{R})$ is not a homomorphism.

Show that $\phi: \mathbb{R^{n}}\to \mathbb{R^{m}}$ defined by $\phi(x)=Ax$ is a homomorphism.

$\mathbb{Z}^k/A\mathbb{Z}^k \cong\mathbb{Z}^k/A'\mathbb{Z}^k$

Is this definition of group homomorphism complete?

Show $\phi$ is a homomorphism, where $(a\star b)_i=a_i+b_{i+\sum_j^p a_j}$

Group Homomorphism: Is it required to have the inverse preservation to prove Identity Mappings?

Is the following claim correct in general?

Find all homomorphisms $\phi: \Bbb{Z}/6\Bbb{Z} \to \Bbb{Z}/15\Bbb{Z}$.

Homomorphism and abelian group.

Homomorphism $ z \rightarrow\frac{z}{|z|}$

How many group homomorphisms between $\mathbb Z_{15}$ and $\mathbb Z_8$

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