Question

Which groups have non-trivial cyclic quotient groups?

score 400 · Answer 1 · 2026-03-28 02:03:27

400

Views

Which groups have non-trivial cyclic quotient groups?

Published on 28 Mar 2026 - 2:03

score 56 · Answer 2 · 2021-09-01 09:03:33

56

Views

When is a surjective hom a retraction?

Published on 01 Sep 2021 - 9:03

score 79 · Answer 3 · 2021-09-01 14:19:04

79

Views

Prove that this abelian group has a subgroup isomorphic to G/H

Published on 01 Sep 2021 - 14:19

score 296 · Answer 4 · 2026-03-26 16:06:58

296

Views

Quotient groups of the Gaussian integers of the form $\mathbb{Z}[i]/ c\mathbb{Z}[i]$

Published on 26 Mar 2026 - 16:06

score 685 · Answer 5 · 2026-03-28 13:41:39

685

Views

$N$ is a simple normal subgroup of a group $G$ and $G/N$ has a composition series...

Published on 28 Mar 2026 - 13:41

score 28 · Answer 6 · 2021-09-02 13:48:20

28

Views

Is there any relation between the grassmannian set and the quotient group

Published on 02 Sep 2021 - 13:48

score 41 · Answer 7 · 2021-09-06 14:21:28

41

Views

Confusion with multiplication when determining the order of $\frac34+\Bbb Z$ in $\Bbb Q/\Bbb Z$.

Published on 06 Sep 2021 - 14:21

score 89 · Answer 8 · 2021-09-14 17:28:39

89

Views

A natural way of thinking about quotient of groups

Published on 14 Sep 2021 - 17:28

score 56 · Answer 9 · 2021-09-16 16:46:20

56

Views

How do I identify the quotient groups in $D_{12}?$

Published on 16 Sep 2021 - 16:46

score 121 · Answer 10 · 2021-09-18 13:11:35

121

Views

Let $G$ be abelian s.t. $r_p(G)<\infty$ if $p=0$ or prime. If $H\le G$, show $r_p(G/H)\le r_0(G)+r_p(G)$ for $p>0$.

Published on 18 Sep 2021 - 13:11

score 109 · Answer 11 · 2026-03-26 06:09:36

109

Views

A homeomorphism to the open upper-half complex plane

Published on 26 Mar 2026 - 6:09

score 76 · Answer 12 · 2021-09-22 20:19:24

76

Views

Let $p$ be odd prime.Why $a,b∈\mathbb Z_p^×-{(\mathbb Z_p^×)}^2$ implies $a/b∈{(\mathbb Z_p^×)}^2$?

Published on 22 Sep 2021 - 20:19

score 176 · Answer 13 · 2021-09-26 16:19:27

176

Views

Let $G$ be abelian s.t. $r_p(G)<\infty$ if $p=0$ or a prime. Prove $G/nG$ is finite for all $n>0$.

Published on 26 Sep 2021 - 16:19

score 100 · Answer 14 · 2021-10-02 22:33:25

100

Views

The structure of $\Bbb Z\times\Bbb Z/H$, where $H=\langle(3,-2)\rangle$

Published on 02 Oct 2021 - 22:33

score 115 · Answer 15 · 2021-10-03 16:31:52

115

Views

If $(g,a) \mapsto g \cdot a$ is an action of $G$ on $A$ and $H \vartriangleleft G$, is $(\overline{g},a) \mapsto g \cdot a$ an action of $G/H$ on $A$?

Published on 03 Oct 2021 - 16:31

List Question

Which groups have non-trivial cyclic quotient groups?

When is a surjective hom a retraction?

Prove that this abelian group has a subgroup isomorphic to G/H

Quotient groups of the Gaussian integers of the form $\mathbb{Z}[i]/ c\mathbb{Z}[i]$

$N$ is a simple normal subgroup of a group $G$ and $G/N$ has a composition series...

Is there any relation between the grassmannian set and the quotient group

Confusion with multiplication when determining the order of $\frac34+\Bbb Z$ in $\Bbb Q/\Bbb Z$.

A natural way of thinking about quotient of groups

How do I identify the quotient groups in $D_{12}?$

Let $G$ be abelian s.t. $r_p(G)<\infty$ if $p=0$ or prime. If $H\le G$, show $r_p(G/H)\le r_0(G)+r_p(G)$ for $p>0$.

A homeomorphism to the open upper-half complex plane

Let $p$ be odd prime.Why $a,b∈\mathbb Z_p^×-{(\mathbb Z_p^×)}^2$ implies $a/b∈{(\mathbb Z_p^×)}^2$?

Let $G$ be abelian s.t. $r_p(G)<\infty$ if $p=0$ or a prime. Prove $G/nG$ is finite for all $n>0$.

The structure of $\Bbb Z\times\Bbb Z/H$, where $H=\langle(3,-2)\rangle$

If $(g,a) \mapsto g \cdot a$ is an action of $G$ on $A$ and $H \vartriangleleft G$, is $(\overline{g},a) \mapsto g \cdot a$ an action of $G/H$ on $A$?

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