List questions from derived-subgroup

Published on 04 Aug 2018 - 12:07

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Does there exist a non-trivial group that is both perfect and complete?

Published on 16 Jun 2019 - 13:24

52

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Does there exist a finite group that is both perfect and immaculate?

Published on 17 Jun 2019 - 9:57

284

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Can a group have a cyclical derived series?

Published on 13 Aug 2019 - 19:07

48

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Is the class of $\omega$-soluble groups a variety?

Published on 27 Aug 2019 - 23:17

5.4k

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Commutator subgroup $G'$ is a characteristic subgroup of $G$

Published on 25 Apr 2014 - 5:17

294

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If the commutator of a finite group has order $2$, then the order of the group is divisible by $8$

Published on 22 Nov 2014 - 17:30

148

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Is $S_6$ the derived subgroup of some group?

Published on 15 Dec 2019 - 1:40

46

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Product of a finite family of derived groups

Published on 19 Mar 2020 - 16:35

27

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Construct normal series from derived series through generating sets

Published on 08 Apr 2020 - 4:23

137

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About -derived subgroup- of a group $G$

Published on 14 Apr 2020 - 0:18

48

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$[G,G] \leq \langle g_1,...,g_{n-1}\rangle$ if and only if $\langle g_1,...,g_{n-1}\rangle$ is normal in $G$

Published on 12 May 2020 - 23:25

1.4k

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If $N$ is a normal subgroup of $G$, and $N \cap [G,G]=\{e\}$, then $N$ is contained in $Z(G)$.

Published on 21 May 2020 - 7:11

214

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Index of commutator subgroup in the commutator group

Published on 08 Jun 2020 - 13:50

64

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How do I find the derived subgroup for this particular group?

Published on 15 Jul 2020 - 3:59

List Question

Any Subgroup containing commutator subgroup is normal.

Does there exist a non-trivial group that is both perfect and complete?

Does there exist a finite group that is both perfect and immaculate?

Can a group have a cyclical derived series?

Is the class of $\omega$-soluble groups a variety?

Commutator subgroup $G'$ is a characteristic subgroup of $G$

If the commutator of a finite group has order $2$, then the order of the group is divisible by $8$

Is $S_6$ the derived subgroup of some group?

Product of a finite family of derived groups

Construct normal series from derived series through generating sets

About -derived subgroup- of a group $G$

$[G,G] \leq \langle g_1,...,g_{n-1}\rangle$ if and only if $\langle g_1,...,g_{n-1}\rangle$ is normal in $G$

If $N$ is a normal subgroup of $G$, and $N \cap [G,G]=\{e\}$, then $N$ is contained in $Z(G)$.

Index of commutator subgroup in the commutator group

How do I find the derived subgroup for this particular group?

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