Question

Prove that the following maps are group homomorphisms. Show that this map is (not) injective and/or (not) surjective.

score 155 · Answer 1 · 2020-07-07 18:51:36

155

Views

Prove that the following maps are group homomorphisms. Show that this map is (not) injective and/or (not) surjective.

Published on 07 Jul 2020 - 18:51

score 64 · Answer 2 · 2020-07-09 19:50:11

64

Views

Number of elements mapped to $f(a)$ where $f$ is a group homomorphism

Published on 09 Jul 2020 - 19:50

score 261 · Answer 3 · 2020-07-10 15:13:40

261

Views

Number of homomorphisms from a subgroup of $S_p$ to $\mathbb Z_p$

Published on 10 Jul 2020 - 15:13

score 74 · Answer 4 · 2020-07-11 01:18:23

74

Views

Proving a group homomorphism

Published on 11 Jul 2020 - 1:18

score 179 · Answer 5 · 2020-07-14 19:02:47

179

Views

Confusion in proving $\phi: Z_n \to Z_k$ defined by $\phi (x)=x \mod k$ to be a homomorphism.

Published on 14 Jul 2020 - 19:02

score 82 · Answer 6 · 2026-03-25 22:04:15

82

Views

A good way to describe a kernel of a group homomorphism

Published on 25 Mar 2026 - 22:04

score 82 · Answer 7 · 2020-07-16 07:41:44

82

Views

Group homomorphism between $\Bbb{Q}$ and $\Bbb{Q}\times\Bbb{Q}$

Published on 16 Jul 2020 - 7:41

score 143 · Answer 8 · 2020-07-16 15:43:59

143

Views

A doubt about Theorem 22 in textbook Algebra by Saunders MacLane and Garrett Birkhoff

Published on 16 Jul 2020 - 15:43

score 53 · Answer 9 · 2020-07-16 23:36:31

53

Views

How to prove that this construction is a group homomorphism?

Published on 16 Jul 2020 - 23:36

score 96 · Answer 10 · 2020-07-17 09:59:55

96

Views

A group homomorphism $\phi: G \rightarrow H$ induces isomorphisms w.r.t intersection and join between $\mathcal G$ and $\mathcal H$

Published on 17 Jul 2020 - 9:59

score 46 · Answer 11 · 2020-07-17 19:48:46

46

Views

Prove that $[G: S]=[\phi [G]: \phi [S]] \cdot[N: S \cap N]$

Published on 17 Jul 2020 - 19:48

score 524 · Answer 12 · 2020-07-17 19:49:56

524

Views

Homomorphism from $\Bbb{Z}_{10}$ to $\Bbb{Z}_5$

Published on 17 Jul 2020 - 19:49

score 73 · Answer 13 · 2020-07-17 20:54:48

73

Views

Infer the second isomorphism theorem from the first one

Published on 17 Jul 2020 - 20:54

score 172 · Answer 14 · 2020-07-17 21:33:23

172

Views

Is it possible to infer the first isomorphism theorem from the second one?

Published on 17 Jul 2020 - 21:33

score 505 · Answer 15 · 2020-07-18 02:02:03

505

Views

The order of the kernel of the $p$th power map of an abelian and noncyclic group of order $p^3$

Published on 18 Jul 2020 - 2:02

List Question

Prove that the following maps are group homomorphisms. Show that this map is (not) injective and/or (not) surjective.

Number of elements mapped to $f(a)$ where $f$ is a group homomorphism

Number of homomorphisms from a subgroup of $S_p$ to $\mathbb Z_p$

Proving a group homomorphism

Confusion in proving $\phi: Z_n \to Z_k$ defined by $\phi (x)=x \mod k$ to be a homomorphism.

A good way to describe a kernel of a group homomorphism

Group homomorphism between $\Bbb{Q}$ and $\Bbb{Q}\times\Bbb{Q}$

A doubt about Theorem 22 in textbook Algebra by Saunders MacLane and Garrett Birkhoff

How to prove that this construction is a group homomorphism?

A group homomorphism $\phi: G \rightarrow H$ induces isomorphisms w.r.t intersection and join between $\mathcal G$ and $\mathcal H$

Prove that $[G: S]=[\phi [G]: \phi [S]] \cdot[N: S \cap N]$

Homomorphism from $\Bbb{Z}_{10}$ to $\Bbb{Z}_5$

Infer the second isomorphism theorem from the first one

Is it possible to infer the first isomorphism theorem from the second one?

The order of the kernel of the $p$th power map of an abelian and noncyclic group of order $p^3$

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