Question

A short question about Hall $\pi$ subgroups

score 96 · Answer 1 · 2020-07-01 13:46:05

96

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A short question about Hall $\pi$ subgroups

Published on 01 Jul 2020 - 13:46

score 1.1k · Answer 2 · 2020-07-10 21:28:04

1.1k

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Let $G$ be a group with order $105 = 3 \cdot 5 \cdot 7$

Published on 10 Jul 2020 - 21:28

score 1.4k · Answer 3 · 2026-03-25 16:03:35

1.4k

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Prove that if $G$ is a finite group in which every proper subgroup is nilpotent, then $G$ is solvable.

Published on 25 Mar 2026 - 16:03

score 222 · Answer 4 · 2020-07-13 09:41:02

222

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Applications of Tits' alternative in number theory

Published on 13 Jul 2020 - 9:41

score 55 · Answer 5 · 2026-02-23 02:14:49

55

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Is it true that the derived series of $G/G^{(n-1)}$ is of length $n-1$, where $n$ is the length of the derived series of $G$?

Published on 23 Feb 2026 - 2:14

score 863 · Answer 6 · 2020-07-16 20:39:49

863

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Let $G$ be a group of order $p^n q$, where $p$ and $q$ are distinct prime. ,

Published on 16 Jul 2020 - 20:39

score 381 · Answer 7 · 2026-03-25 06:03:53

381

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Let $G$ be a finite non-solvable group, each of whose proper subgroups is solvable.

Published on 25 Mar 2026 - 6:03

score 720 · Answer 8 · 2020-07-21 19:33:07

720

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Let $G$ be a finite group such that if $A, B\le G$ then $AB\le G$. Prove $G$ is a solvable.

Published on 21 Jul 2020 - 19:33

score 328 · Answer 9 · 2020-07-22 17:30:45

328

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A finite group $G$ is called an $N$-group if the normalizer $N_G(P)$ of every non-identity p-subgroup $P$ of $G$ is solvable.

Published on 22 Jul 2020 - 17:30

score 68 · Answer 10 · 2026-03-25 06:27:43

68

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Practical algorithm to calculate power subgroup of a polycyclic group

Published on 25 Mar 2026 - 6:27

score 112 · Answer 11 · 2020-07-28 17:38:48

112

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Which solvable Lie algebras / groups occur as Borel of semisimple Lie algebras / groups?

Published on 28 Jul 2020 - 17:38

score 2.9k · Answer 12 · 2016-08-10 07:00:08

2.9k

Views

Every normal subgroup of a solvable group must have an abelian subgroup which is normal in G.

Published on 10 Aug 2016 - 7:00

score 393 · Answer 13 · 2016-08-12 16:24:37

393

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Conditions under which group solvability is invariant under an homomorphism.

Published on 12 Aug 2016 - 16:24

score 101 · Answer 14 · 2016-08-12 17:36:56

101

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$G/K$ is solvable $\iff G^{n}⊆K$

Published on 12 Aug 2016 - 17:36

score 62 · Answer 15 · 2016-08-15 20:38:08

62

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Group theory: $l(G \times H) = l(G) + l(H)$ and $fact(G \times H) = fact(G) \cup fact(H)$

Published on 15 Aug 2016 - 20:38

List Question

A short question about Hall $\pi$ subgroups

Let $G$ be a group with order $105 = 3 \cdot 5 \cdot 7$

Prove that if $G$ is a finite group in which every proper subgroup is nilpotent, then $G$ is solvable.

Applications of Tits' alternative in number theory

Is it true that the derived series of $G/G^{(n-1)}$ is of length $n-1$, where $n$ is the length of the derived series of $G$?

Let $G$ be a group of order $p^n q$, where $p$ and $q$ are distinct prime. ,

Let $G$ be a finite non-solvable group, each of whose proper subgroups is solvable.

Let $G$ be a finite group such that if $A, B\le G$ then $AB\le G$. Prove $G$ is a solvable.

A finite group $G$ is called an $N$-group if the normalizer $N_G(P)$ of every non-identity p-subgroup $P$ of $G$ is solvable.

Practical algorithm to calculate power subgroup of a polycyclic group

Which solvable Lie algebras / groups occur as Borel of semisimple Lie algebras / groups?

Every normal subgroup of a solvable group must have an abelian subgroup which is normal in G.

Conditions under which group solvability is invariant under an homomorphism.

$G/K$ is solvable $\iff G^{n}⊆K$

Group theory: $l(G \times H) = l(G) + l(H)$ and $fact(G \times H) = fact(G) \cup fact(H)$

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