List questions from nilpotent-groups

Published on 15 Apr 2026 - 16:36

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An Infinite non-nilpotent group whose every maximal subgroup is a normal subgroup.

Published on 13 Apr 2026 - 21:20

97

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A generalizaton of nilpotent groups

Published on 12 Apr 2026 - 5:15

110

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Let $G$ be a nilpotent group, $H\subsetneq G$. How to prove $H \subsetneq N$, where $N$ is a normalizer of $H$?

Published on 13 Apr 2026 - 10:51

245

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Show that if an $n \times n$ matrix, $A$, is nilpotent, then $\text{rank}(A) < n$

Published on 16 Apr 2026 - 4:11

128

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Is this an equivalent definition of a nilpotent group?

Published on 11 Apr 2026 - 18:09

78

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Nilpotent Matrices Questions.

Published on 11 Apr 2026 - 2:12

136

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Every (finite) group having a central series is nilpotent.

Published on 12 Apr 2026 - 9:59

49

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Give an example of a solvable group of prime exponent which is not nilpotent.

Published on 12 Apr 2026 - 2:11

115

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The rank of torsion free nilpotent group

Published on 14 Apr 2026 - 22:58

207

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Characterization of a virtually nilpotent group

Published on 11 Apr 2026 - 15:03

58

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Semidirect product is supersolvable groups

Published on 10 Apr 2026 - 18:19

152

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Having trouble understanding nilpotent and supersolvable group in terms of short exact sequence

Published on 09 Apr 2026 - 18:52

281

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Nilpotent groups can be constructed by means of abelian groups.

Published on 10 May 2026 - 16:56

40

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ith Center of Product is Product of ith Centers

Published on 12 Apr 2026 - 23:55

List Question

Is it true that if $\mathrm{Aut}(G)$ is nilpotent then $G$ is also nilpotent?

An Infinite non-nilpotent group whose every maximal subgroup is a normal subgroup.

A generalizaton of nilpotent groups

Let $G$ be a nilpotent group, $H\subsetneq G$. How to prove $H \subsetneq N$, where $N$ is a normalizer of $H$?

Show that if an $n \times n$ matrix, $A$, is nilpotent, then $\text{rank}(A) < n$

Is this an equivalent definition of a nilpotent group?

Nilpotent Matrices Questions.

Every (finite) group having a central series is nilpotent.

Give an example of a solvable group of prime exponent which is not nilpotent.

The rank of torsion free nilpotent group

Characterization of a virtually nilpotent group

Semidirect product is supersolvable groups

Having trouble understanding nilpotent and supersolvable group in terms of short exact sequence

Nilpotent groups can be constructed by means of abelian groups.

ith Center of Product is Product of ith Centers

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