List questions from derived-subgroup

Published on 28 Feb 2024 - 19:42

84

Views

Does there exist an element of order $4$ in $GL_2(\mathbb{Z})/GL_2(\mathbb{Z})'$?

Published on 06 Mar 2024 - 11:13

147

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When is the center of group contained in the derived subgroup

Published on 17 Mar 2024 - 9:17

35

Views

Commutator Subgroup of Thompson's Group F

Published on 25 Mar 2024 - 10:27

11.4k

Views

Calculating the commutator (derived) subgroup of $S_3$

Published on 02 Sep 2015 - 10:32

677

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Show $S_4$ can't be derived group

Published on 01 Dec 2013 - 22:17

9k

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Commutator subgroup of a dihedral group.

Published on 05 Dec 2013 - 2:53

3.9k

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Commutator Subgroup and the Largest Abelian Quotient

Published on 12 Dec 2013 - 3:31

2.3k

Views

Generators of the first commutator subgroup

Published on 09 Mar 2014 - 12:39

1.4k

Views

Proving a commutator identity for groups

Published on 30 Oct 2011 - 11:16

2.4k

Views

Show that $[G,G]$ is a normal subgroup of $G.$

Published on 18 Oct 2020 - 6:36

114

Views

If $G$ is a finite group with $G'<G$, then $G$ has a normal subgroup of prime index.

Published on 23 Oct 2020 - 23:12

220

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If $G$ is finite of odd order, then the product of all its elements, in any order, is an element of the commutator subgroup $G'$.

Published on 31 Oct 2020 - 22:54

82

Views

Show that $\forall n \in \mathbb N^+:G^{(n)}\trianglelefteq G^{(n-1)}$

Published on 05 Nov 2020 - 9:41

1.3k

Views

$G$ is Abelian if and only if $[e,e]$ is the only commutator of $G$

Published on 05 Nov 2020 - 9:58

List Question

Proving the isomorphism type of the commutator subgroup of the dihedral group $D_n$

Does there exist an element of order $4$ in $GL_2(\mathbb{Z})/GL_2(\mathbb{Z})'$?

When is the center of group contained in the derived subgroup

Commutator Subgroup of Thompson's Group F

Calculating the commutator (derived) subgroup of $S_3$

Show $S_4$ can't be derived group

Commutator subgroup of a dihedral group.

Commutator Subgroup and the Largest Abelian Quotient

Generators of the first commutator subgroup

Proving a commutator identity for groups

Show that $[G,G]$ is a normal subgroup of $G.$

If $G$ is a finite group with $G'<G$, then $G$ has a normal subgroup of prime index.

If $G$ is finite of odd order, then the product of all its elements, in any order, is an element of the commutator subgroup $G'$.

Show that $\forall n \in \mathbb N^+:G^{(n)}\trianglelefteq G^{(n-1)}$

$G$ is Abelian if and only if $[e,e]$ is the only commutator of $G$

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