Question

Relation between set of Normal subgroups and set of Homomorphism images of a group $G$

score 392 · Answer 1 · 2018-12-29 13:10:55

392

Views

Relation between set of Normal subgroups and set of Homomorphism images of a group $G$

Published on 29 Dec 2018 - 13:10

score 107 · Answer 2 · 2018-12-29 15:54:32

107

Views

There exists an element of order $5$ in $G$

Published on 29 Dec 2018 - 15:54

score 102 · Answer 3 · 2018-12-30 11:22:17

102

Views

How is it possible that $\textrm{HK}=\textrm{G}$?

Published on 30 Dec 2018 - 11:22

score 814 · Answer 4 · 2026-03-25 06:05:52

814

Views

Understanding semidirect product by constructing a non-abelian group of order $21$

Published on 25 Mar 2026 - 6:05

score 45 · Answer 5 · 2018-12-31 15:20:25

45

Views

Prove the following permutation mapping is a homomorphism.

Published on 31 Dec 2018 - 15:20

score 44 · Answer 6 · 2019-01-03 19:18:24

44

Views

Showing that $o(\phi(g))|o(g)$ if $\phi:G_1\mapsto G_2$ is a homomorphism and $g\in G_1$

Published on 03 Jan 2019 - 19:18

score 53 · Answer 7 · 2019-01-04 13:16:07

53

Views

When is it true that $\nexists g\ne e$ such that $\phi(g)=e$ for a group homomorphism $\phi: G\mapsto H$ and $|H|\not\mid|G|$?

Published on 04 Jan 2019 - 13:16

score 394 · Answer 8 · 2026-03-26 01:14:34

394

Views

Construct a non trivial homomorphism from $\mathbb{Z}_2\times\mathbb{Z}_4$ to $\mathbb{Z}_8$

Published on 26 Mar 2026 - 1:14

score 51 · Answer 9 · 2019-01-05 19:06:43

51

Views

Why is the kernel of $\phi : G\mapsto S_m$ included in $B\le G$ where $\phi(g)=g:xB\mapsto gxB$?

Published on 05 Jan 2019 - 19:06

score 55 · Answer 10 · 2019-01-07 18:15:14

55

Views

Verifying a statement related to group homomorphism

Published on 07 Jan 2019 - 18:15

score 70 · Answer 11 · 2026-03-25 10:53:37

70

Views

Counterexample for Converse of Surjective Homomorphisms

Published on 25 Mar 2026 - 10:53

score 259 · Answer 12 · 2019-01-19 19:55:33

259

Views

Normal subgroup and corresponding homomorphism

Published on 19 Jan 2019 - 19:55

score 36 · Answer 13 · 2019-01-20 11:37:03

36

Views

Isomorphism relation in $Hom(\mathbb{Z}_6,\mathbb{R}^\oplus\mathbb{C}^)?$

Published on 20 Jan 2019 - 11:37

score 870 · Answer 14 · 2019-01-21 14:31:50

870

Views

Homomorphisms of $S_3$

Published on 21 Jan 2019 - 14:31

score 136 · Answer 15 · 2019-01-23 20:45:11

136

Views

Find all homomorphism from $S_4$ to $z_m$.

Published on 23 Jan 2019 - 20:45

List Question

Relation between set of Normal subgroups and set of Homomorphism images of a group $G$

There exists an element of order $5$ in $G$

How is it possible that $\textrm{HK}=\textrm{G}$?

Understanding semidirect product by constructing a non-abelian group of order $21$

Prove the following permutation mapping is a homomorphism.

Showing that $o(\phi(g))|o(g)$ if $\phi:G_1\mapsto G_2$ is a homomorphism and $g\in G_1$

When is it true that $\nexists g\ne e$ such that $\phi(g)=e$ for a group homomorphism $\phi: G\mapsto H$ and $|H|\not\mid|G|$?

Construct a non trivial homomorphism from $\mathbb{Z}_2\times\mathbb{Z}_4$ to $\mathbb{Z}_8$

Why is the kernel of $\phi : G\mapsto S_m$ included in $B\le G$ where $\phi(g)=g:xB\mapsto gxB$?

Verifying a statement related to group homomorphism

Counterexample for Converse of Surjective Homomorphisms

Normal subgroup and corresponding homomorphism

Isomorphism relation in $Hom(\mathbb{Z}_6,\mathbb{R}^\oplus\mathbb{C}^)?$

Homomorphisms of $S_3$

Find all homomorphism from $S_4$ to $z_m$.

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