Question

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 $G$?

score 54 · Answer 1 · 2020-07-15 17:16:17

54

Views

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 15 Jul 2020 - 17:16

score 141 · Answer 2 · 2026-02-22 22:38:13

141

Views

The commutator of Holomorph of generalized quaternion is abelian?

Published on 22 Feb 2026 - 22:38

score 47 · Answer 3 · 2023-04-14 14:05:49

47

Views

What is known about this generalisation of the derived group?

Published on 14 Apr 2023 - 14:05

score 72 · Answer 4 · 2023-05-05 15:19:15

72

Views

Testing if an element is in the derived subgroup

Published on 05 May 2023 - 15:19

score 80 · Answer 5 · 2023-05-16 23:52:40

80

Views

If $G/G’ $ is cyclic, prove by induction that $G/Z(G)$ is cyclic if $G$ is $p$ group.

Published on 16 May 2023 - 23:52

score 57 · Answer 6 · 2023-06-07 08:31:07

57

Views

If $G^{(i)}$ denotes the ith derived subgroup of $G$ then $G^{(i+1)}$ is a proper subgroup of $G^{(i)}$

Published on 07 Jun 2023 - 8:31

score 125 · Answer 7 · 2023-06-28 14:30:58

125

Views

When is the special linear group $SL_n(\Bbb F_q)$ over a finite field $\Bbb F_q$ solvable?

Published on 28 Jun 2023 - 14:30

score 105 · Answer 8 · 2023-07-13 12:44:56

105

Views

$G$ finite metabelian group, $P$ a Sylow $p$-subgroup. Show that $P'$ is abelian and normal in $G$

Published on 13 Jul 2023 - 12:44

score 75 · Answer 9 · 2023-07-19 09:03:07

75

Views

Solvable Groups and Derived Subgroups. Why does $D(G_i) \subset G_{i + 1} \implies D_i(G) \subset G_i$.

Published on 19 Jul 2023 - 9:03

score 80 · Answer 10 · 2023-08-19 12:27:04

80

Views

Prove/disprove: Let $G$ s.t $|G| = p^3 \implies |G'| \leq p$.

Published on 19 Aug 2023 - 12:27

score 75 · Answer 11 · 2023-08-27 12:21:49

75

Views

The only proper normal subgroups of a nonabelian quasisimple group are subgroups of its centre.

Published on 27 Aug 2023 - 12:21

score 39 · Answer 12 · 2023-11-05 11:24:59

39

Views

$R$ points of derived subgroup of algebraic group

Published on 05 Nov 2023 - 11:24

score 76 · Answer 13 · 2023-11-19 00:48:22

76

Views

Commutator Subgroup is a Subgroup of "$G^2$"

Published on 19 Nov 2023 - 0:48

score 109 · Answer 14 · 2023-12-16 03:49:17

109

Views

What is the relationship between Inner Automorphism group and Commutator subgroup? Why are they both about commutativity?

Published on 16 Dec 2023 - 3:49

score 103 · Answer 15 · 2024-01-21 02:12:05

103

Views

proving a commutator identity

Published on 21 Jan 2024 - 2:12

List Question

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 $G$?

The commutator of Holomorph of generalized quaternion is abelian?

What is known about this generalisation of the derived group?

Testing if an element is in the derived subgroup

If $G/G’ $ is cyclic, prove by induction that $G/Z(G)$ is cyclic if $G$ is $p$ group.

If $G^{(i)}$ denotes the ith derived subgroup of $G$ then $G^{(i+1)}$ is a proper subgroup of $G^{(i)}$

When is the special linear group $SL_n(\Bbb F_q)$ over a finite field $\Bbb F_q$ solvable?

$G$ finite metabelian group, $P$ a Sylow $p$-subgroup. Show that $P'$ is abelian and normal in $G$

Solvable Groups and Derived Subgroups. Why does $D(G_i) \subset G_{i + 1} \implies D_i(G) \subset G_i$.

Prove/disprove: Let $G$ s.t $|G| = p^3 \implies |G'| \leq p$.

The only proper normal subgroups of a nonabelian quasisimple group are subgroups of its centre.

$R$ points of derived subgroup of algebraic group

Commutator Subgroup is a Subgroup of "$G^2$"

What is the relationship between Inner Automorphism group and Commutator subgroup? Why are they both about commutativity?

proving a commutator identity

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