Question

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

score 73 · Answer 1 · 2026-04-17 01:04:28

73

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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 17 Apr 2026 - 1:04

score 66 · Answer 2 · 2026-04-08 23:36:17

66

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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 08 Apr 2026 - 23:36

score 388 · Answer 3 · 2026-04-14 11:33:48

388

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

Published on 14 Apr 2026 - 11:33

score 29 · Answer 4 · 2026-04-12 09:57:29

29

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Equivalent definition of nilpotency for infinite groups

Published on 12 Apr 2026 - 9:57

score 93 · Answer 5 · 2026-04-13 20:55:45

93

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Example of nilpotent profinite group

Published on 13 Apr 2026 - 20:55

score 130 · Answer 6 · 2026-04-14 23:40:43

130

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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 14 Apr 2026 - 23:40

score 107 · Answer 7 · 2026-04-13 21:40:05

107

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

Published on 13 Apr 2026 - 21:40

score 321 · Answer 8 · 2026-04-15 04:19:20

321

Views

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

Published on 15 Apr 2026 - 4:19

score 183 · Answer 9 · 2026-04-12 10:58:55

183

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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 12 Apr 2026 - 10:58

score 95 · Answer 10 · 2026-04-14 08:34:34

95

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

Published on 14 Apr 2026 - 8:34

score 117 · Answer 11 · 2026-04-07 23:48:33

117

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An association between finite nilpotent groups and Lie rings

Published on 07 Apr 2026 - 23:48

score 208 · Answer 12 · 2026-04-16 13:55:52

208

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p-nilpotent group and p-Fitting subgroup

Published on 16 Apr 2026 - 13:55

score 127 · Answer 13 · 2026-04-12 01:54:10

127

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Is every group of order $136$ nilpotent?

Published on 12 Apr 2026 - 1:54

score 77 · Answer 14 · 2026-04-11 18:49:49

77

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

Published on 11 Apr 2026 - 18:49

score 98 · Answer 15 · 2026-04-13 07:42:40

98

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Solvability, nilpotence and permutation Groups

Published on 13 Apr 2026 - 7:42

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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