List questions from nilpotent-groups

Published on 11 Jan 2022 - 3:41

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If $N\unlhd G$ is nilpotent and $G/N'$ is supersolvable, then $G$ is supersolvable.

Published on 26 Jan 2022 - 19:22

97

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Self-centralizing subgroups of order $p^2$ in $p$-groups of maximal class

Published on 08 Feb 2022 - 21:59

113

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(renamed) Torsion free group has finite commutator subgroup iff abelian

Published on 14 Feb 2022 - 17:48

83

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What are some "easy, transcendental" constructions of finite nilpotent groups?

Published on 02 Mar 2022 - 18:26

249

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On nilpotent groups of class 2

Published on 27 Mar 2022 - 3:59

93

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Each element of a nilpotent group is nilpotent

Published on 02 Apr 2022 - 13:39

68

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Let $G_1=G/Z(G)$ for a group $G$. Let $G_{i}$ be the group $G_{i-1}/Z(G_{i-1})$. If $G_{k}/Z(G_{k})$ is abelian, is $G$ nilpotent?

Published on 13 Apr 2022 - 18:07

124

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Dummit and Foote 6.1.2

Published on 17 Apr 2022 - 3:22

136

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Quotient of a non-elementary nilponent group

Published on 14 May 2022 - 7:53

230

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Is it true that the center of a finitely generated nilpotent group is finitely generated?

Published on 24 May 2022 - 6:57

65

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an Equivalent condition for nilpotency of a finite group like of finite solvable group

Published on 24 May 2022 - 16:21

183

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Is it true that nilpotent always has some eigenvalue?

Published on 04 Jun 2022 - 23:30

113

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How do subgroups of the inner automorphisms of a group look like?

Published on 08 Jun 2022 - 10:53

61

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Characterization of finite nilpotent groups

Published on 09 Jun 2022 - 11:02

List Question

Proof Verification: $G/Z(G)$ is nilpotent implies $G$ is nilpotent

If $N\unlhd G$ is nilpotent and $G/N'$ is supersolvable, then $G$ is supersolvable.

Self-centralizing subgroups of order $p^2$ in $p$-groups of maximal class

(renamed) Torsion free group has finite commutator subgroup iff abelian

What are some "easy, transcendental" constructions of finite nilpotent groups?

On nilpotent groups of class 2

Each element of a nilpotent group is nilpotent

Let $G_1=G/Z(G)$ for a group $G$. Let $G_{i}$ be the group $G_{i-1}/Z(G_{i-1})$. If $G_{k}/Z(G_{k})$ is abelian, is $G$ nilpotent?

Dummit and Foote 6.1.2

Quotient of a non-elementary nilponent group

Is it true that the center of a finitely generated nilpotent group is finitely generated?

an Equivalent condition for nilpotency of a finite group like of finite solvable group

Is it true that nilpotent always has some eigenvalue?

How do subgroups of the inner automorphisms of a group look like?

Characterization of finite nilpotent groups

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