Question

Existence of injective and surjective group homomorphisms in both directions implies existence of group isomorphism

score 252 · Answer 1 · 2024-02-02 14:34:57

252

Views

Existence of injective and surjective group homomorphisms in both directions implies existence of group isomorphism

Published on 02 Feb 2024 - 14:34

score 110 · Answer 2 · 2024-02-04 07:35:21

110

Views

Constructing a nontrivial action of $A_{4}$ on $S$ with $|S| = 3$.

Published on 04 Feb 2024 - 7:35

score 173 · Answer 3 · 2024-02-06 22:50:19

173

Views

For every subgroup $H$ of a finite abelian group $ G$ there exist an endomorphism $\phi$ with $\text{Im}(\phi)=H$

Published on 06 Feb 2024 - 22:50

score 38 · Answer 4 · 2024-02-08 03:24:32

38

Views

Injective $\mathbb{C}$-vector space homomorphism $V\to W$ iff surjective homomorphism $W\to V$.

Published on 08 Feb 2024 - 3:24

score 117 · Answer 5 · 2024-02-10 21:58:04

117

Views

If $G$ is abelian and $\varphi:G\to H$ is a non-trivial homomorphism, then does $H$ have to be Abelian?

Published on 10 Feb 2024 - 21:58

score 57 · Answer 6 · 2024-02-21 23:45:36

57

Views

Proof that cardinality of inverse image will always be the same for a particular group homomorphism

Published on 21 Feb 2024 - 23:45

score 54 · Answer 7 · 2024-02-24 21:18:20

54

Views

Problem of finding an optimal weak homomorphism between two graphs

Published on 24 Feb 2024 - 21:18

score 89 · Answer 8 · 2024-02-29 03:43:37

89

Views

Showing There is No Group Epimorphism from $S_n \longrightarrow \mathbb{Z}/2\times\mathbb{Z}/2$, $n\geq 1$

Published on 29 Feb 2024 - 3:43

score 74 · Answer 9 · 2024-03-02 06:07:54

74

Views

Determine the number of group homomorphisms $f:\mathbb Z_{63}\to\mathbb Z_{147}$ with $|image(f)|=7$.

Published on 02 Mar 2024 - 6:07

score 32 · Answer 10 · 2024-03-11 19:11:22

32

Views

Metric properties of graphs of lie groups homomorphisms

Published on 11 Mar 2024 - 19:11

score 23 · Answer 11 · 2026-03-27 10:08:22

23

Views

extension condition for free abelian groups

Published on 27 Mar 2026 - 10:08

score 40 · Answer 12 · 2026-03-26 13:50:39

40

Views

All module homomorphisms from $\mathbb{Z}^n$ to $\mathbb{Z}$

Published on 26 Mar 2026 - 13:50

score 79 · Answer 13 · 2024-03-18 11:43:47

79

Views

Let $G$ be a finite abelian group of order n. How many distinct group homomorphisms are there from $G$ to $R/Z$?

Published on 18 Mar 2024 - 11:43

score 23 · Answer 14 · 2026-03-26 11:18:00

23

Views

Huppert, III.19.2: How to construct a homomorphism from a $p$-group into the center of a maximal subgroup?

Published on 26 Mar 2026 - 11:18

score 79 · Answer 15 · 2026-03-25 22:09:11

79

Views

Munkres' Topology theorem 68.7

Published on 25 Mar 2026 - 22:09

List Question

Existence of injective and surjective group homomorphisms in both directions implies existence of group isomorphism

Constructing a nontrivial action of $A_{4}$ on $S$ with $|S| = 3$.

For every subgroup $H$ of a finite abelian group $ G$ there exist an endomorphism $\phi$ with $\text{Im}(\phi)=H$

Injective $\mathbb{C}$-vector space homomorphism $V\to W$ iff surjective homomorphism $W\to V$.

If $G$ is abelian and $\varphi:G\to H$ is a non-trivial homomorphism, then does $H$ have to be Abelian?

Proof that cardinality of inverse image will always be the same for a particular group homomorphism

Problem of finding an optimal weak homomorphism between two graphs

Showing There is No Group Epimorphism from $S_n \longrightarrow \mathbb{Z}/2\times\mathbb{Z}/2$, $n\geq 1$

Determine the number of group homomorphisms $f:\mathbb Z_{63}\to\mathbb Z_{147}$ with $|image(f)|=7$.

Metric properties of graphs of lie groups homomorphisms

extension condition for free abelian groups

All module homomorphisms from $\mathbb{Z}^n$ to $\mathbb{Z}$

Let $G$ be a finite abelian group of order n. How many distinct group homomorphisms are there from $G$ to $R/Z$?

Huppert, III.19.2: How to construct a homomorphism from a $p$-group into the center of a maximal subgroup?

Munkres' Topology theorem 68.7

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