Question

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

score 65 · Answer 1 · 2026-04-16 00:25:54

65

Views

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

Published on 16 Apr 2026 - 0:25

score 117 · Answer 2 · 2026-04-11 07:50:34

117

Views

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

Published on 11 Apr 2026 - 7:50

score 166 · Answer 3 · 2026-04-16 05:48:06

166

Views

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

Published on 16 Apr 2026 - 5:48

score 38 · Answer 4 · 2026-04-14 16:03:55

38

Views

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

Published on 14 Apr 2026 - 16:03

score 69 · Answer 5 · 2026-04-13 14:43:04

69

Views

Property preserved by tensor product/ epimorphic image/ extension

Published on 13 Apr 2026 - 14:43

score 48 · Answer 6 · 2026-04-11 21:41:52

48

Views

References on Nilpotent groups of class 2

Published on 11 Apr 2026 - 21:41

score 167 · Answer 7 · 2026-04-15 23:20:50

167

Views

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

Published on 15 Apr 2026 - 23:20

score 68 · Answer 8 · 2026-04-10 09:08:25

68

Views

Is upper central series of a group unique?

Published on 10 Apr 2026 - 9:08

score 82 · Answer 9 · 2026-04-13 21:12:16

82

Views

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

Published on 13 Apr 2026 - 21:12

score 85 · Answer 10 · 2026-04-16 10:41:13

85

Views

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

Published on 16 Apr 2026 - 10:41

score 69 · Answer 11 · 2026-04-12 03:52:08

69

Views

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

Published on 12 Apr 2026 - 3:52

score 675 · Answer 12 · 2026-04-16 06:21:50

675

Views

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

Published on 16 Apr 2026 - 6:21

score 81 · Answer 13 · 2026-04-12 20:39:56

81

Views

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

Published on 12 Apr 2026 - 20:39

score 218 · Answer 14 · 2026-04-13 11:58:16

218

Views

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

Published on 13 Apr 2026 - 11:58

score 67 · Answer 15 · 2026-04-12 20:15:08

67

Views

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

Published on 12 Apr 2026 - 20:15

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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