Question

If $G$ is a nilpotent torsion group of nilpotence class $c$, then $\exp(G)$ divides $\exp(G^{\operatorname{ab}})^c$

score 70 · Answer 1 · 2021-05-23 21:28:22

70

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If $G$ is a nilpotent torsion group of nilpotence class $c$, then $\exp(G)$ divides $\exp(G^{\operatorname{ab}})^c$

Published on 23 May 2021 - 21:28

score 64 · Answer 2 · 2021-06-09 15:14:41

64

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

Published on 09 Jun 2021 - 15:14

score 385 · Answer 3 · 2021-06-10 10:14:12

385

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

Published on 10 Jun 2021 - 10:14

score 26 · Answer 4 · 2021-06-11 07:27:22

26

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Equivalent definition of nilpotency for infinite groups

Published on 11 Jun 2021 - 7:27

score 90 · Answer 5 · 2021-06-11 17:49:46

90

Views

Example of nilpotent profinite group

Published on 11 Jun 2021 - 17:49

score 127 · Answer 6 · 2021-06-13 17:19:58

127

Views

Let $G$ be a finite group, $H\leq G$ s. t. $\forall g\in G$, either $\langle H, H^g \rangle$ is nilpotent or $H H^g = H^g H$. Show that $H \lhd\lhd G$

Published on 13 Jun 2021 - 17:19

score 104 · Answer 7 · 2021-06-24 14:17:50

104

Views

Proving nilpotency class of certain subgroup is less than nilpotency class of group

Published on 24 Jun 2021 - 14:17

score 318 · Answer 8 · 2026-02-23 07:48:07

318

Views

If $G$ is a nilpotent group and $H\leq G$ with $H[G,G]=G$ then $H=G$.

Published on 23 Feb 2026 - 7:48

score 180 · Answer 9 · 2021-08-21 21:17:17

180

Views

Given $p$ prime and $H\le S_p$ s.t. $|H| = p$, show if $H\subseteq N\subseteq S_p$ for some nilpotent subgroup $N$, then $H=N$

Published on 21 Aug 2021 - 21:17

score 92 · Answer 10 · 2021-08-24 12:13:55

92

Views

Direct Product of a nilpotent group with a supersolvable group is supersolvable

Published on 24 Aug 2021 - 12:13

score 115 · Answer 11 · 2021-08-24 14:13:58

115

Views

An association between finite nilpotent groups and Lie rings

Published on 24 Aug 2021 - 14:13

score 205 · Answer 12 · 2021-08-26 00:38:56

205

Views

p-nilpotent group and p-Fitting subgroup

Published on 26 Aug 2021 - 0:38

score 124 · Answer 13 · 2021-08-27 21:17:00

124

Views

Is every group of order $136$ nilpotent?

Published on 27 Aug 2021 - 21:17

score 74 · Answer 14 · 2021-08-30 01:28:46

74

Views

If $|H| = p$ s.t. $H<N<S_p$ where $N$ is nilpotent, then $H = N$.

Published on 30 Aug 2021 - 1:28

score 95 · Answer 15 · 2021-09-02 06:13:01

95

Views

Solvability, nilpotence and permutation Groups

Published on 02 Sep 2021 - 6:13

List Question

If $G$ is a nilpotent torsion group of nilpotence class $c$, then $\exp(G)$ divides $\exp(G^{\operatorname{ab}})^c$

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

Equivalent definition of nilpotency for infinite groups

Example of nilpotent profinite group

Let $G$ be a finite group, $H\leq G$ s. t. $\forall g\in G$, either $\langle H, H^g \rangle$ is nilpotent or $H H^g = H^g H$. Show that $H \lhd\lhd G$

Proving nilpotency class of certain subgroup is less than nilpotency class of group

If $G$ is a nilpotent group and $H\leq G$ with $H[G,G]=G$ then $H=G$.

Given $p$ prime and $H\le S_p$ s.t. $|H| = p$, show if $H\subseteq N\subseteq S_p$ for some nilpotent subgroup $N$, then $H=N$

Direct Product of a nilpotent group with a supersolvable group is supersolvable

An association between finite nilpotent groups and Lie rings

p-nilpotent group and p-Fitting subgroup

Is every group of order $136$ nilpotent?

If $|H| = p$ s.t. $H<N<S_p$ where $N$ is nilpotent, then $H = N$.

Solvability, nilpotence and permutation Groups

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