List questions from derived-subgroup

Published on 16 Aug 2021 - 22:20

84

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Let $H\leq G$ s.t. whenever 2 elements of $G$ are conjugate then the conjugating element can be chosen from within $H$. Prove that $G'\subseteq H$.

Published on 25 Aug 2021 - 18:52

196

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Non-existence of perfect groups with order $180$

Published on 28 Sep 2021 - 20:02

38

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Information about $P'$ in $P \rtimes Q$

Published on 01 Oct 2021 - 11:37

87

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Why $G'' \triangleleft G$?

Published on 15 Oct 2021 - 2:47

106

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why "this means that $G'' \subset Z(G')$"?

Published on 15 Oct 2021 - 11:14

34

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If $G$ nilpotent and $G/G'$ is cyclic then $G$ is cyclic?

Published on 23 Nov 2021 - 14:57

574

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The relationship between the commutator subgroup and the center of a group

Published on 10 Jan 2022 - 20:00

151

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If every finitely generated subgroup of a linear group G is solvable, then G is solvable

Published on 14 Jan 2022 - 10:56

605

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Let $G$ be a group, $H\unlhd G$, prove that the commutator subgroup $H'$ of $H$ is a normal subgroup in $G$.

Published on 08 Feb 2022 - 17:31

48

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Intersection of the derived subgroup with a cyclic group

Published on 16 Feb 2022 - 19:31

40

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Given $H \lhd G$ and $G/H$ is abelian then the derived group $G'$ or $[G,G]$ satisfies $G'\subseteq H$

Published on 28 Mar 2022 - 21:27

594

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How to find the derived subgroup of a given group

Published on 28 Mar 2022 - 22:18

781

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How to find the derived subgroup of $Q_8$

Published on 29 Mar 2022 - 0:17

95

Views

Is there an easy way to find the derived group of $S_5$?

Published on 29 Mar 2022 - 1:08

List Question

If $G$ is a nilpotent group and $H\leq G$ with $H[G,G]=G$ then $H=G$.

Let $H\leq G$ s.t. whenever 2 elements of $G$ are conjugate then the conjugating element can be chosen from within $H$. Prove that $G'\subseteq H$.

Non-existence of perfect groups with order $180$

Information about $P'$ in $P \rtimes Q$

Why $G'' \triangleleft G$?

why "this means that $G'' \subset Z(G')$"?

If $G$ nilpotent and $G/G'$ is cyclic then $G$ is cyclic?

The relationship between the commutator subgroup and the center of a group

If every finitely generated subgroup of a linear group G is solvable, then G is solvable

Let $G$ be a group, $H\unlhd G$, prove that the commutator subgroup $H'$ of $H$ is a normal subgroup in $G$.

Intersection of the derived subgroup with a cyclic group

Given $H \lhd G$ and $G/H$ is abelian then the derived group $G'$ or $[G,G]$ satisfies $G'\subseteq H$

How to find the derived subgroup of a given group

How to find the derived subgroup of $Q_8$

Is there an easy way to find the derived group of $S_5$?

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