Question

Quotient of the Baumslag-Solitar group $BS(1,m)=\langle a,b| bab^{-1}=a^m\rangle$.

score 650 · Answer 1 · 2015-06-01 10:42:24

650

Views

Quotient of the Baumslag-Solitar group $BS(1,m)=\langle a,b| bab^{-1}=a^m\rangle$.

Published on 01 Jun 2015 - 10:42

score 1.8k · Answer 2 · 2015-09-17 16:10:27

1.8k

Views

Prove $D_{2n}/\langle r^k\rangle$ is isomorphic to $D_{2k}$

Published on 17 Sep 2015 - 16:10

score 173 · Answer 3 · 2015-10-14 08:35:52

173

Views

Let $ G $ be a group and $ N \lhd G $. Why is $G $ supersoluble if $ N $ is cyclic and $ G/N $ is supersoluble?

Published on 14 Oct 2015 - 8:35

score 61 · Answer 4 · 2015-11-19 00:44:03

61

Views

Show a homomorphism between groups induces a homomorphish between their respective quotient groups

Published on 19 Nov 2015 - 0:44

score 1.9k · Answer 5 · 2026-03-16 08:56:24

1.9k

Views

Is there an equivalence between representations of $N$ and $G/N$, and a representation of $G$?

Published on 16 Mar 2026 - 8:56

score 78 · Answer 6 · 2026-03-25 16:31:38

78

Views

Let $L$ be a subgroup of $\mathbb{Z}^3$ of index $16$. What are the possibilities for $\mathbb{Z}^3 /L$?

Published on 25 Mar 2026 - 16:31

score 70 · Answer 7 · 2026-03-07 10:56:25

70

Views

Let $G=\langle X\mid R\rangle$ and $H=\langle X\mid S\rangle$. If $R\subseteq S$, the $H$ is isomorphic to a quotient of $G$.

Published on 07 Mar 2026 - 10:56

score 363 · Answer 8 · 2016-04-19 18:21:03

363

Views

If $G/Z(G)$ is cyclic, why is $G$ only abelian and not also cyclic?

Published on 19 Apr 2016 - 18:21

score 670 · Answer 9 · 2013-09-13 04:31:53

670

Views

Why not introduce quotient groups this way?

Published on 13 Sep 2013 - 4:31

score 4.5k · Answer 10 · 2013-11-11 01:41:14

4.5k

Views

Why is $D_4/Z(D_4)$ "just like" $V$, Klein's 4-group?

Published on 11 Nov 2013 - 1:41

score 59 · Answer 11 · 2013-12-02 07:40:43

59

Views

$G$ has a copy of $G/N$

Published on 02 Dec 2013 - 7:40

score 3.9k · Answer 12 · 2026-02-23 03:57:38

3.9k

Views

Commutator Subgroup and the Largest Abelian Quotient

Published on 23 Feb 2026 - 3:57

score 79 · Answer 13 · 2017-04-10 17:03:26

79

Views

What are the cosets of this subgroup of the affine group?

Published on 10 Apr 2017 - 17:03

score 334 · Answer 14 · 2017-04-12 22:13:22

334

Views

$x+\mathbb{Z}$ has finite order iff $x\in \mathbb{Q}$

Published on 12 Apr 2017 - 22:13

score 958 · Answer 15 · 2017-05-02 16:07:14

958

Views

Show that is not possible to form a unity ring structure on $(\Bbb Q /\Bbb Z , + )$

Published on 02 May 2017 - 16:07

List Question

Quotient of the Baumslag-Solitar group $BS(1,m)=\langle a,b| bab^{-1}=a^m\rangle$.

Prove $D_{2n}/\langle r^k\rangle$ is isomorphic to $D_{2k}$

Let $ G $ be a group and $ N \lhd G $. Why is $G $ supersoluble if $ N $ is cyclic and $ G/N $ is supersoluble?

Show a homomorphism between groups induces a homomorphish between their respective quotient groups

Is there an equivalence between representations of $N$ and $G/N$, and a representation of $G$?

Let $L$ be a subgroup of $\mathbb{Z}^3$ of index $16$. What are the possibilities for $\mathbb{Z}^3 /L$?

Let $G=\langle X\mid R\rangle$ and $H=\langle X\mid S\rangle$. If $R\subseteq S$, the $H$ is isomorphic to a quotient of $G$.

If $G/Z(G)$ is cyclic, why is $G$ only abelian and not also cyclic?

Why not introduce quotient groups this way?

Why is $D_4/Z(D_4)$ "just like" $V$, Klein's 4-group?

$G$ has a copy of $G/N$

Commutator Subgroup and the Largest Abelian Quotient

What are the cosets of this subgroup of the affine group?

$x+\mathbb{Z}$ has finite order iff $x\in \mathbb{Q}$

Show that is not possible to form a unity ring structure on $(\Bbb Q /\Bbb Z , + )$

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