Question

If $G$ is nilpotent of class $n$, then $G/Z(G)$ is nilpotent of class $n−1$.

score 62 · Answer 1 · 2023-04-17 15:35:49

62

Views

If $G$ is nilpotent of class $n$, then $G/Z(G)$ is nilpotent of class $n−1$.

Published on 17 Apr 2023 - 15:35

score 114 · Answer 2 · 2023-06-13 02:24:38

114

Views

Non-Abelian group of exponent $3$ and Nilpotent class $2$ .

Published on 13 Jun 2023 - 2:24

score 163 · Answer 3 · 2023-06-13 15:47:09

163

Views

Commutator of two elements in group algebra $\mathbb F_{5}D_{30}.$

Published on 13 Jun 2023 - 15:47

score 35 · Answer 4 · 2023-06-14 05:18:16

35

Views

Some calculation in $F_5[D_{30}]$.

Published on 14 Jun 2023 - 5:18

score 66 · Answer 5 · 2023-07-14 16:23:48

66

Views

Property preserved by tensor product/ epimorphic image/ extension

Published on 14 Jul 2023 - 16:23

score 45 · Answer 6 · 2023-07-24 12:10:53

45

Views

References on Nilpotent groups of class 2

Published on 24 Jul 2023 - 12:10

score 164 · Answer 7 · 2023-08-04 21:27:48

164

Views

If $G$ is a finite group in which every subgroup has a normal complement, then $G$ is nilpotent.

Published on 04 Aug 2023 - 21:27

score 65 · Answer 8 · 2023-08-27 17:51:21

65

Views

Is upper central series of a group unique?

Published on 27 Aug 2023 - 17:51

score 79 · Answer 9 · 2023-09-04 02:22:59

79

Views

A different approach to proving a property of nilpotent injectors in solvable groups

Published on 04 Sep 2023 - 2:22

score 82 · Answer 10 · 2023-11-13 02:29:41

82

Views

If $G/Z(G)$ is nilpotent, then $G$ is nilpotent

Published on 13 Nov 2023 - 2:29

score 66 · Answer 11 · 2023-12-06 09:11:55

66

Views

The existence of a matrix $B$ with $AB=BA^c$ implies nilpotence of $A^r-I$.

Published on 06 Dec 2023 - 9:11

score 672 · Answer 12 · 2023-12-28 01:33:05

672

Views

Is there an analogue of the abelianization of a group for nilpotent groups?

Published on 28 Dec 2023 - 1:33

score 78 · Answer 13 · 2024-01-14 13:20:27

78

Views

Non-nilpotent group where the union of the upper central groups equals the whole group

Published on 14 Jan 2024 - 13:20

score 215 · Answer 14 · 2024-01-14 14:44:56

215

Views

Finitely generated, nilpotent, torsion-free group that is also radicable

Published on 14 Jan 2024 - 14:44

score 64 · Answer 15 · 2024-01-24 00:13:28

64

Views

Is there an infinite nilpotent group with one Sylow subgroup that is not normal?

Published on 24 Jan 2024 - 0:13

List Question

If $G$ is nilpotent of class $n$, then $G/Z(G)$ is nilpotent of class $n−1$.

Non-Abelian group of exponent $3$ and Nilpotent class $2$ .

Commutator of two elements in group algebra $\mathbb F_{5}D_{30}.$

Some calculation in $F_5[D_{30}]$.

Property preserved by tensor product/ epimorphic image/ extension

References on Nilpotent groups of class 2

If $G$ is a finite group in which every subgroup has a normal complement, then $G$ is nilpotent.

Is upper central series of a group unique?

A different approach to proving a property of nilpotent injectors in solvable groups

If $G/Z(G)$ is nilpotent, then $G$ is nilpotent

The existence of a matrix $B$ with $AB=BA^c$ implies nilpotence of $A^r-I$.

Is there an analogue of the abelianization of a group for nilpotent groups?

Non-nilpotent group where the union of the upper central groups equals the whole group

Finitely generated, nilpotent, torsion-free group that is also radicable

Is there an infinite nilpotent group with one Sylow subgroup that is not normal?

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