Question

The attributes of the defined direct product.

score 31 · Answer 1 · 2018-03-17 18:37:44

31

Views

The attributes of the defined direct product.

Published on 17 Mar 2018 - 18:37

score 120 · Answer 2 · 2018-03-17 21:38:49

120

Views

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

Published on 17 Mar 2018 - 21:38

score 72 · Answer 3 · 2018-03-18 07:41:41

72

Views

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

Published on 18 Mar 2018 - 7:41

score 426 · Answer 4 · 2018-03-19 01:16:47

426

Views

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

Published on 19 Mar 2018 - 1:16

score 72 · Answer 5 · 2018-03-19 02:52:29

72

Views

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

Published on 19 Mar 2018 - 2:52

score 179 · Answer 6 · 2018-03-19 16:16:02

179

Views

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

Published on 19 Mar 2018 - 16:16

score 40 · Answer 7 · 2018-03-23 17:44:55

40

Views

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

Published on 23 Mar 2018 - 17:44

score 40 · Answer 8 · 2018-03-24 08:21:19

40

Views

Is this definition of group homomorphism complete?

Published on 24 Mar 2018 - 8:21

score 67 · Answer 9 · 2018-03-27 11:02:23

67

Views

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

Published on 27 Mar 2018 - 11:02

score 358 · Answer 10 · 2018-03-28 11:14:37

358

Views

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

Published on 28 Mar 2018 - 11:14

score 116 · Answer 11 · 2018-03-30 09:54:12

116

Views

Is the following claim correct in general?

Published on 30 Mar 2018 - 9:54

score 3.3k · Answer 12 · 2026-03-25 01:17:41

3.3k

Views

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

Published on 25 Mar 2026 - 1:17

score 67 · Answer 13 · 2026-03-25 06:08:26

67

Views

Homomorphism and abelian group.

Published on 25 Mar 2026 - 6:08

score 152 · Answer 14 · 2018-04-04 08:47:48

152

Views

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

Published on 04 Apr 2018 - 8:47

score 54 · Answer 15 · 2018-04-05 02:36:24

54

Views

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

Published on 05 Apr 2018 - 2:36

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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