Question

$H \subseteq K$ be subgroups of an infinite abelian group $G$ such that $G/H \cong G/K$ , then are $H,K$ equal or atleast isomorphic?

score 163 · Answer 1 · 2026-03-26 06:32:38

163

Views

$H \subseteq K$ be subgroups of an infinite abelian group $G$ such that $G/H \cong G/K$ , then are $H,K$ equal or atleast isomorphic?

Published on 26 Mar 2026 - 6:32

score 102 · Answer 2 · 2016-07-19 18:25:30

102

Views

Does there exist a multiplicative $f:\mathbb{Q}^+\to\mathbb{Q}^+$ such that $f\neq x\mapsto x^a$ for all $a$?

Published on 19 Jul 2016 - 18:25

score 1.8k · Answer 3 · 2016-07-22 18:06:11

1.8k

Views

Kernel of homomorphism is normal subgroup

Published on 22 Jul 2016 - 18:06

score 7k · Answer 4 · 2016-07-24 14:40:13

7k

Views

All homomorphisms from $Z/4Z$ to $Z/6Z$

Published on 24 Jul 2016 - 14:40

score 1.6k · Answer 5 · 2016-07-25 14:22:02

1.6k

Views

Homomorphism between S4 and A4

Published on 25 Jul 2016 - 14:22

score 171 · Answer 6 · 2016-08-01 12:14:05

171

Views

Let $f: G \to H$ be a group homomorphism with $|\ker(f)|=2$. Show that every element of $H$ has no preimage or exactly $2$ preimages under $f$.

Published on 01 Aug 2016 - 12:14

score 1.2k · Answer 7 · 2016-08-02 02:58:09

1.2k

Views

Question about image of homomorphism from $\mathbb{R}$ to $GL(2,\mathbb{R})$

Published on 02 Aug 2016 - 2:58

score 72 · Answer 8 · 2026-03-27 14:03:25

72

Views

The relationship between the order of an element in a group and the order of its image

Published on 27 Mar 2026 - 14:03

score 177 · Answer 9 · 2016-08-05 08:38:12

177

Views

Need help with understanding $f^{-1}$ when $f$ is a homomorphism

Published on 05 Aug 2016 - 8:38

score 2k · Answer 10 · 2016-08-05 18:14:54

2k

Views

Quaternions Group Homomorphic to Klein Group

Published on 05 Aug 2016 - 18:14

score 1.3k · Answer 11 · 2016-08-06 15:09:39

1.3k

Views

Homomorphisms between Dihedral and Cyclic Groups

Published on 06 Aug 2016 - 15:09

score 390 · Answer 12 · 2026-03-26 04:52:06

390

Views

Is $(\mathbb Q^+, . )$ isomorphic with a subgroup of $(\mathbb R,+)$ ?

Published on 26 Mar 2026 - 4:52

score 1.2k · Answer 13 · 2026-03-26 04:51:23

1.2k

Views

Does there exist any surjective group homomorphism from $(\mathbb R^* , .)$ onto $(\mathbb Q^* , .)$?

Published on 26 Mar 2026 - 4:51

score 614 · Answer 14 · 2016-08-20 04:32:58

614

Views

If $f:G\rightarrow G'$ is a homomorphism, then prove $f^{-1}(H')$, where $H' < G'$, is a subgroup of $G$

Published on 20 Aug 2016 - 4:32

score 233 · Answer 15 · 2026-03-26 17:42:26

233

Views

If $|G| = 1920$ and $|H| = 80$ are groups, $f:G \rightarrow H$ epimorphism then $G$ is solvable.

Published on 26 Mar 2026 - 17:42

List Question

$H \subseteq K$ be subgroups of an infinite abelian group $G$ such that $G/H \cong G/K$ , then are $H,K$ equal or atleast isomorphic?

Does there exist a multiplicative $f:\mathbb{Q}^+\to\mathbb{Q}^+$ such that $f\neq x\mapsto x^a$ for all $a$?

Kernel of homomorphism is normal subgroup

All homomorphisms from $Z/4Z$ to $Z/6Z$

Homomorphism between S4 and A4

Let $f: G \to H$ be a group homomorphism with $|\ker(f)|=2$. Show that every element of $H$ has no preimage or exactly $2$ preimages under $f$.

Question about image of homomorphism from $\mathbb{R}$ to $GL(2,\mathbb{R})$

The relationship between the order of an element in a group and the order of its image

Need help with understanding $f^{-1}$ when $f$ is a homomorphism

Quaternions Group Homomorphic to Klein Group

Homomorphisms between Dihedral and Cyclic Groups

Is $(\mathbb Q^+, . )$ isomorphic with a subgroup of $(\mathbb R,+)$ ?

Does there exist any surjective group homomorphism from $(\mathbb R^* , .)$ onto $(\mathbb Q^* , .)$?

If $f:G\rightarrow G'$ is a homomorphism, then prove $f^{-1}(H')$, where $H' < G'$, is a subgroup of $G$

If $|G| = 1920$ and $|H| = 80$ are groups, $f:G \rightarrow H$ epimorphism then $G$ is solvable.

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