Question

Soluble group with arbitrary derived length

score 87 · Answer 1 · 2021-04-10 23:15:54

87

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Soluble group with arbitrary derived length

Published on 10 Apr 2021 - 23:15

score 318 · Answer 2 · 2021-04-17 00:15:44

318

Views

Is it true that any non-solvable group cannot be a subgroup of a solvable group?

Published on 17 Apr 2021 - 0:15

score 2.1k · Answer 3 · 2021-04-17 21:24:03

2.1k

Views

A proof for Abelian groups are solvable

Published on 17 Apr 2021 - 21:24

score 55 · Answer 4 · 2021-04-28 20:18:37

55

Views

Index of normal subgroup in a normal series

Published on 28 Apr 2021 - 20:18

score 99 · Answer 5 · 2021-05-12 21:57:16

99

Views

Why is $\Bbb{Z}_2 \times A_5$ not solvable?

Published on 12 May 2021 - 21:57

score 108 · Answer 6 · 2021-05-20 10:09:34

108

Views

Prove: $G^{(m)}=\{e\}$, as $G^{(m)}$ is the $m$th commutator subgroup of $|G|=p^n$ for a prime $p$, and $m\ge \frac{1}{2}n$

Published on 20 May 2021 - 10:09

score 103 · Answer 7 · 2021-05-21 16:50:32

103

Views

Find all composition factors of a group of order $780$ that is not solvable.

Published on 21 May 2021 - 16:50

score 1.2k · Answer 8 · 2021-05-26 04:46:04

1.2k

Views

Definitions of solvable group

Published on 26 May 2021 - 4:46

score 76 · Answer 9 · 2021-05-26 18:11:09

76

Views

Character degrees of solvable group

Published on 26 May 2021 - 18:11

score 19 · Answer 10 · 2026-03-24 19:01:04

19

Views

Show that if ${\frak h}\oplus x\Bbb F$ is solvabe and $e_0$ is a simultaneous eigenvector, then $\pi(x)^pe_0$ are all in the same eigenspace

Published on 24 Mar 2026 - 19:01

score 60 · Answer 11 · 2021-06-01 14:39:59

60

Views

Order of quotient group for an infinite soluble group

Published on 01 Jun 2021 - 14:39

score 202 · Answer 12 · 2026-03-27 22:07:53

202

Views

Is there a solvable differential equation with a nonsolvable lie group of symmetries?

Published on 27 Mar 2026 - 22:07

score 65 · Answer 13 · 2026-03-26 06:30:59

65

Views

Let $H=\langle\sigma\rangle$ be the infinite cyclic group. Consider $G = (\mathbb{Z}\times \mathbb{Z})\rtimes H$. Determine $G'$.

Published on 26 Mar 2026 - 6:30

score 386 · Answer 14 · 2026-03-26 06:31:43

386

Views

Nilpotent quotient of semidirect product of a nilpotent group and a free abelian group

Published on 26 Mar 2026 - 6:31

score 193 · Answer 15 · 2021-06-10 22:04:00

193

Views

Let $G$ be a group and $H$ solvable subgroup of index smaller or equal to $4.$ Show $G$ is a solvable group.

Published on 10 Jun 2021 - 22:04

List Question

Soluble group with arbitrary derived length

Is it true that any non-solvable group cannot be a subgroup of a solvable group?

A proof for Abelian groups are solvable

Index of normal subgroup in a normal series

Why is $\Bbb{Z}_2 \times A_5$ not solvable?

Prove: $G^{(m)}=\{e\}$, as $G^{(m)}$ is the $m$th commutator subgroup of $|G|=p^n$ for a prime $p$, and $m\ge \frac{1}{2}n$

Find all composition factors of a group of order $780$ that is not solvable.

Definitions of solvable group

Character degrees of solvable group

Show that if ${\frak h}\oplus x\Bbb F$ is solvabe and $e_0$ is a simultaneous eigenvector, then $\pi(x)^pe_0$ are all in the same eigenspace

Order of quotient group for an infinite soluble group

Is there a solvable differential equation with a nonsolvable lie group of symmetries?

Let $H=\langle\sigma\rangle$ be the infinite cyclic group. Consider $G = (\mathbb{Z}\times \mathbb{Z})\rtimes H$. Determine $G'$.

Nilpotent quotient of semidirect product of a nilpotent group and a free abelian group

Let $G$ be a group and $H$ solvable subgroup of index smaller or equal to $4.$ Show $G$ is a solvable group.

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