List questions from nilpotent-groups

Published on 12 Nov 2012 - 13:47

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

Published on 03 Aug 2020 - 15:00

94

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A generalizaton of nilpotent groups

Published on 04 Sep 2020 - 20:19

107

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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 22 Sep 2020 - 19:11

242

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

Published on 23 Sep 2020 - 1:24

125

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Is this an equivalent definition of a nilpotent group?

Published on 27 Sep 2020 - 5:08

75

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Nilpotent Matrices Questions.

Published on 08 Oct 2020 - 16:14

133

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

Published on 16 Oct 2020 - 19:24

46

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

Published on 28 Oct 2020 - 5:36

112

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The rank of torsion free nilpotent group

Published on 12 Nov 2020 - 0:42

204

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Characterization of a virtually nilpotent group

Published on 12 Nov 2020 - 7:38

55

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Semidirect product is supersolvable groups

Published on 19 Nov 2020 - 21:16

150

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

Published on 27 Nov 2020 - 22:16

280

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Nilpotent groups can be constructed by means of abelian groups.

Published on 25 Mar 2026 - 4:40

37

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ith Center of Product is Product of ith Centers

Published on 10 Dec 2020 - 3:28

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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