Question

Find a certain group $G$ with $H,K\unlhd G$, $H\cong K$ and $(G/H)\ncong(G/K)$

score 64 · Answer 1 · 2020-11-28 16:03:20

64

Views

Find a certain group $G$ with $H,K\unlhd G$, $H\cong K$ and $(G/H)\ncong(G/K)$

Published on 28 Nov 2020 - 16:03

score 507 · Answer 2 · 2020-11-30 15:01:50

507

Views

Prove that the Galois group $G = Gal(x^5-2; \mathbb{Q})$ is a group metacyclic.

Published on 30 Nov 2020 - 15:01

score 448 · Answer 3 · 2020-12-02 21:02:30

448

Views

Is this explanation of normal subgroups and quotient groups correct?

Published on 02 Dec 2020 - 21:02

score 235 · Answer 4 · 2026-03-26 22:55:36

235

Views

Rank of the quotient of an Abelian group by its torsion part?

Published on 26 Mar 2026 - 22:55

score 307 · Answer 5 · 2020-12-05 00:08:05

307

Views

Find a property of groups that is inherited by quotients but not by subgroups.

Published on 05 Dec 2020 - 0:08

score 134 · Answer 6 · 2020-12-06 00:31:15

134

Views

Find a property of groups that is inherited by subgroups but not by quotients.

Published on 06 Dec 2020 - 0:31

score 348 · Answer 7 · 2020-12-07 11:10:08

348

Views

Group homomorphism between quotient groups.

Published on 07 Dec 2020 - 11:10

score 89 · Answer 8 · 2020-12-09 03:53:42

89

Views

Counterexample to problem regarding Hall $\pi$-subgroups of a quotient group

Published on 09 Dec 2020 - 3:53

score 184 · Answer 9 · 2020-12-10 16:39:45

184

Views

$G/N = 1$ iff $N = G$ and $G/N = G$ iff $N = 1$

Published on 10 Dec 2020 - 16:39

score 1.4k · Answer 10 · 2020-12-11 13:17:42

1.4k

Views

If $G/H$ is cyclic, where $H$ is a subgroup of $Z(G)$, then $G$ is abelian.

Published on 11 Dec 2020 - 13:17

score 66 · Answer 11 · 2020-12-14 23:48:06

66

Views

If $N,K\in\mathcal{F}$ are subgroups of $G$ with $K\unlhd G$, then $NK\in\mathcal{F}$.

Published on 14 Dec 2020 - 23:48

score 67 · Answer 12 · 2020-12-19 19:50:24

67

Views

Let $H\le G$ with $|G:H|=n<\infty$. Let $\varpi$ be the set of all primes not exceeding $n$. Then $G/H_G$ is a finite $\varpi$-group

Published on 19 Dec 2020 - 19:50

score 91 · Answer 13 · 2020-12-20 04:35:43

91

Views

Finding a normal subgroup of a fiber product giving a prescribed quotient.

Published on 20 Dec 2020 - 4:35

score 667 · Answer 14 · 2020-12-20 20:18:54

667

Views

How to prove that a quotient group is isomorphic to a group of matrices

Published on 20 Dec 2020 - 20:18

score 61 · Answer 15 · 2020-12-28 09:42:28

61

Views

$G=D_8$ and $H=\langle r^2 \rangle $ why is $G/H \cong \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$

Published on 28 Dec 2020 - 9:42

List Question

Find a certain group $G$ with $H,K\unlhd G$, $H\cong K$ and $(G/H)\ncong(G/K)$

Prove that the Galois group $G = Gal(x^5-2; \mathbb{Q})$ is a group metacyclic.

Is this explanation of normal subgroups and quotient groups correct?

Rank of the quotient of an Abelian group by its torsion part?

Find a property of groups that is inherited by quotients but not by subgroups.

Find a property of groups that is inherited by subgroups but not by quotients.

Group homomorphism between quotient groups.

Counterexample to problem regarding Hall $\pi$-subgroups of a quotient group

$G/N = 1$ iff $N = G$ and $G/N = G$ iff $N = 1$

If $G/H$ is cyclic, where $H$ is a subgroup of $Z(G)$, then $G$ is abelian.

If $N,K\in\mathcal{F}$ are subgroups of $G$ with $K\unlhd G$, then $NK\in\mathcal{F}$.

Let $H\le G$ with $|G:H|=n<\infty$. Let $\varpi$ be the set of all primes not exceeding $n$. Then $G/H_G$ is a finite $\varpi$-group

Finding a normal subgroup of a fiber product giving a prescribed quotient.

How to prove that a quotient group is isomorphic to a group of matrices

$G=D_8$ and $H=\langle r^2 \rangle $ why is $G/H \cong \mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$

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