List questions from normal-subgroups

81

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Is the subgroup $H:=\langle xyxy\rangle$ normal in $G:=\langle x,y\mid x^3=e, y^2=e\rangle$? If so, find $G/H$.

Published on 18 Mar 2026 - 23:56

35

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Generating elements of a subgroup

Published on 21 Mar 2016 - 1:50

143

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what does it mean that a subgroup self-normalizes?

Published on 21 Mar 2016 - 10:01

559

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Definition normal subgroups

Published on 21 Mar 2016 - 16:21

1k

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Find the normal and the composition series

Published on 27 Mar 2026 - 23:38

1.2k

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Each minimal normal subgroup of is contained in the center

Published on 27 Mar 2026 - 4:23

43

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How to show that there are just $n$ cosets for the $n\mathbb{Z}$ relation?

Published on 29 Mar 2016 - 0:54

590

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Isomorphism of Quotient Subgroups

Published on 31 Mar 2016 - 6:46

132

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Show that $G$ is nilpotent when the quotient group is nilpotent

Published on 27 Mar 2026 - 4:23

412

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$G$ contains a normal $p$-subgroup

Published on 27 Mar 2026 - 3:46

74

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Biggest noncommutative group $N$ where a group $G$ is normal.

Published on 03 Apr 2016 - 1:50

680

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Is a union of cosets of a normal subgroup a subgroup itself?

Published on 03 Apr 2016 - 19:07

164

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if HK is a subgroup for all K, does it imply that H is normal?

Published on 05 Apr 2016 - 10:32

72

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Proof that every group of order $15,400$ has a normal subgroup of order $275$

Published on 05 Apr 2016 - 14:47

1.4k

Views

Subgroups of special linear group SL$(n, \mathbb{Z})$

Published on 26 Mar 2026 - 4:32

List Question

Is the subgroup $H:=\langle xyxy\rangle$ normal in $G:=\langle x,y\mid x^3=e, y^2=e\rangle$? If so, find $G/H$.

Generating elements of a subgroup

what does it mean that a subgroup self-normalizes?

Definition normal subgroups

Find the normal and the composition series

Each minimal normal subgroup of is contained in the center

How to show that there are just $n$ cosets for the $n\mathbb{Z}$ relation?

Isomorphism of Quotient Subgroups

Show that $G$ is nilpotent when the quotient group is nilpotent

$G$ contains a normal $p$-subgroup

Biggest noncommutative group $N$ where a group $G$ is normal.

Is a union of cosets of a normal subgroup a subgroup itself?

if HK is a subgroup for all K, does it imply that H is normal?

Proof that every group of order $15,400$ has a normal subgroup of order $275$

Subgroups of special linear group SL$(n, \mathbb{Z})$

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