Question

Finite Engel group is nilpotent.

score 350 · Answer 1 · 2019-01-03 09:47:04

350

Views

Finite Engel group is nilpotent.

Published on 03 Jan 2019 - 9:47

score 1.1k · Answer 2 · 2019-01-20 17:07:57

1.1k

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$G$ with a central series that is different from the upper and the lower central series

Published on 20 Jan 2019 - 17:07

score 73 · Answer 3 · 2019-01-23 07:13:13

73

Views

If $\operatorname{class}(G) = 2$ and $\exp(G) = 4$ then $\exp(G') = 2$?

Published on 23 Jan 2019 - 7:13

score 201 · Answer 4 · 2019-01-23 17:53:42

201

Views

$D_4 \times \mathbb{Z}_2$ different upper and lower central series

Published on 23 Jan 2019 - 17:53

score 327 · Answer 5 · 2026-03-25 04:39:41

327

Views

A question about Frattini subgroup of specific form

Published on 25 Mar 2026 - 4:39

score 27 · Answer 6 · 2019-01-28 15:25:34

27

Views

Relationship between Carnot-Caratheory Distance and Levi-Civita Connection

Published on 28 Jan 2019 - 15:25

score 82 · Answer 7 · 2019-03-02 11:15:22

Let $\zeta_{i}G$ be the upper central series of G. Why does the definition of central series imply that $H\zeta_{i}G$ is normal in $H\zeta_{i+1}G$.?

score 307 · Answer 8 · 2019-03-06 16:21:57

307

Views

Why all nilpotent and finitely generated groups are Max?

Published on 06 Mar 2019 - 16:21

score 54 · Answer 9 · 2026-03-25 03:02:20

54

Views

A question about Frattini subgroup of specific form v2.0

Published on 25 Mar 2026 - 3:02

score 386 · Answer 10 · 2019-03-22 17:02:36

386

Views

Let $G$ be a $p$-group of nilpotency class at most 2, where $p$ is an odd prime. Then ${\{x^p| x \in G\}}$ is a subgroup of $G$.

Published on 22 Mar 2019 - 17:02

score 31 · Answer 11 · 2026-03-22 12:59:10

31

Views

Existence of a nilpotent subgroup $N \leq G$ of step $\leq n$ such that a finite $A$ is in $K^{O_n(1)}$ left cosets of $N$

Published on 22 Mar 2026 - 12:59

score 74 · Answer 12 · 2019-04-11 23:24:33

74

Views

Let $G$ be a nilpotent group prove that for each $x \in Z_2(G)$ the map $\theta_x: G \rightarrow Z(G)$ defined by $\theta_x(g)=[g,x]$ is a hom

Published on 11 Apr 2019 - 23:24

score 184 · Answer 13 · 2026-03-19 15:02:17

184

Views

Growth rate of finitely generated nilpotent groups

Published on 19 Mar 2026 - 15:02

score 61 · Answer 14 · 2019-04-14 18:13:34

61

Views

Finitely generated nilpotent group is isomorphic to a quotient of the free nilpotent group.

Published on 14 Apr 2019 - 18:13

score 65 · Answer 15 · 2019-04-16 14:35:42

65

Views

If $G$ is $s$-step nilpotent and $n \in \mathbb N$, then $(G_s)^{n^s} \subset (G^n)_s \subset (G_s)^n$

Published on 16 Apr 2019 - 14:35

List Question

Finite Engel group is nilpotent.

$G$ with a central series that is different from the upper and the lower central series

If $\operatorname{class}(G) = 2$ and $\exp(G) = 4$ then $\exp(G') = 2$?

$D_4 \times \mathbb{Z}_2$ different upper and lower central series

A question about Frattini subgroup of specific form

Relationship between Carnot-Caratheory Distance and Levi-Civita Connection

Let $\zeta_{i}G$ be the upper central series of G. Why does the definition of central series imply that $H\zeta_{i}G$ is normal in $H\zeta_{i+1}G$.?

Why all nilpotent and finitely generated groups are Max?

A question about Frattini subgroup of specific form v2.0

Let $G$ be a $p$-group of nilpotency class at most 2, where $p$ is an odd prime. Then ${\{x^p| x \in G\}}$ is a subgroup of $G$.

Existence of a nilpotent subgroup $N \leq G$ of step $\leq n$ such that a finite $A$ is in $K^{O_n(1)}$ left cosets of $N$

Let $G$ be a nilpotent group prove that for each $x \in Z_2(G)$ the map $\theta_x: G \rightarrow Z(G)$ defined by $\theta_x(g)=[g,x]$ is a hom

Growth rate of finitely generated nilpotent groups

Finitely generated nilpotent group is isomorphic to a quotient of the free nilpotent group.

If $G$ is $s$-step nilpotent and $n \in \mathbb N$, then $(G_s)^{n^s} \subset (G^n)_s \subset (G_s)^n$

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