Question

Given f: GXH--G f(x, y) = x and h: GXH--H h(x, y) = y show f and h are homomorphism of the group's GXH, G, and H.

score 127 · Answer 1 · 2019-12-08 19:39:11

127

Views

Given f: GXH--G f(x, y) = x and h: GXH--H h(x, y) = y show f and h are homomorphism of the group's GXH, G, and H.

Published on 08 Dec 2019 - 19:39

score 77 · Answer 2 · 2019-12-12 02:02:04

77

Views

Prove that $\phi$ is a homomorphism.

Published on 12 Dec 2019 - 2:02

score 229 · Answer 3 · 2019-12-13 06:31:38

229

Views

For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?

Published on 13 Dec 2019 - 6:31

score 789 · Answer 4 · 2019-12-13 22:35:08

789

Views

If $H$ is a subgroup of $G$ and contains all commutators $aba^{-1}b^{-1}$ with $a, b \in G$, then $H$ is normal.

Published on 13 Dec 2019 - 22:35

score 287 · Answer 5 · 2019-12-14 19:10:49

287

Views

Cyclic group and homomorphism

Published on 14 Dec 2019 - 19:10

score 717 · Answer 6 · 2019-12-15 21:33:33

717

Views

If composition of homomorphisms is an isomorphism, then the constituent homomorphisms are also isomorphisms

Published on 15 Dec 2019 - 21:33

score 433 · Answer 7 · 2019-12-16 16:26:29

433

Views

Show that if $H$ is any group and $h\in H$ and $|h|=n$ then there is a homomorphism from $\mathbb{Z}_n=\langle x\rangle$ to H such that $x\mapsto h$

Published on 16 Dec 2019 - 16:26

score 46 · Answer 8 · 2019-12-18 05:08:13

46

Views

What is the implicit operation for power sets in the context of groups?

Published on 18 Dec 2019 - 5:08

score 120 · Answer 9 · 2026-03-26 03:11:25

120

Views

Conditions to check for homomorphism described on generators and relations

Published on 26 Mar 2026 - 3:11

score 351 · Answer 10 · 2019-12-18 23:48:13

351

Views

Find all group homomorphisms from $\mathbb{Q}$ to $GL_n(\mathbb{C})$

Published on 18 Dec 2019 - 23:48

score 120 · Answer 11 · 2019-12-19 20:52:04

120

Views

Field/Group Homomorphisms $\mathbb{Z}/3\mathbb{Z} \to \mathbb{Z}/5\mathbb{Z}$

Published on 19 Dec 2019 - 20:52

score 76 · Answer 12 · 2019-12-20 17:19:49

76

Views

Show that $f:\Bbb{F}_3[x]\to\Bbb{F}_3[x]$ given by $a(x)\mapsto a(x)^3$ is a group homomorphism.

Published on 20 Dec 2019 - 17:19

score 1.7k · Answer 13 · 2019-12-21 03:55:09

1.7k

Views

How to show that $\phi(g)=g^{-1}$ is a group homomorphism iff $G$ is abelian?

Published on 21 Dec 2019 - 3:55

score 582 · Answer 14 · 2019-12-22 07:25:47

582

Views

Homomorphism to abelian group

Published on 22 Dec 2019 - 7:25

score 3.2k · Answer 15 · 2019-12-23 18:01:11

3.2k

Views

If $H$ and $K$ are subgroups of $G$, and $K$ is normal, then $HK$ is a subgroup of $G$

Published on 23 Dec 2019 - 18:01

List Question

Given f: GXH--G f(x, y) = x and h: GXH--H h(x, y) = y show f and h are homomorphism of the group's GXH, G, and H.

Prove that $\phi$ is a homomorphism.

For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?

If $H$ is a subgroup of $G$ and contains all commutators $aba^{-1}b^{-1}$ with $a, b \in G$, then $H$ is normal.

Cyclic group and homomorphism

If composition of homomorphisms is an isomorphism, then the constituent homomorphisms are also isomorphisms

Show that if $H$ is any group and $h\in H$ and $|h|=n$ then there is a homomorphism from $\mathbb{Z}_n=\langle x\rangle$ to H such that $x\mapsto h$

What is the implicit operation for power sets in the context of groups?

Conditions to check for homomorphism described on generators and relations

Find all group homomorphisms from $\mathbb{Q}$ to $GL_n(\mathbb{C})$

Field/Group Homomorphisms $\mathbb{Z}/3\mathbb{Z} \to \mathbb{Z}/5\mathbb{Z}$

Show that $f:\Bbb{F}_3[x]\to\Bbb{F}_3[x]$ given by $a(x)\mapsto a(x)^3$ is a group homomorphism.

How to show that $\phi(g)=g^{-1}$ is a group homomorphism iff $G$ is abelian?

Homomorphism to abelian group

If $H$ and $K$ are subgroups of $G$, and $K$ is normal, then $HK$ is a subgroup of $G$

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