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Question about Reynold's operator of a subgroup

score 90 · Answer 1 · 2020-02-11 09:19:03

90

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Question about Reynold's operator of a subgroup

Published on 11 Feb 2020 - 9:19

score 1.1k · Answer 2 · 2020-02-11 09:27:28

1.1k

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Index of a subgroup in $SL_2(\mathbb{Z})$

Published on 11 Feb 2020 - 9:27

score 83 · Answer 3 · 2026-03-29 00:05:39

83

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Checking a normal subgroup of $S_4$

Published on 29 Mar 2026 - 0:05

score 367 · Answer 4 · 2026-03-26 16:06:10

367

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Proving that subgroup of Rotations in $D_{2n}$ is a normal subgroup

Published on 26 Mar 2026 - 16:06

score 72 · Answer 5 · 2026-03-25 14:25:19

72

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Let $G = \{A \in G L_n(\mathbb{R}) : \mathrm{det} A = 2^k$ for some $k \in Z \}$. Show that $G$ is a normal subgroup of $H = GL_n(\mathbb{R})$.

Published on 25 Mar 2026 - 14:25

score 66 · Answer 6 · 2020-02-17 12:49:52

66

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Proving a property of normal subgroups.

Published on 17 Feb 2020 - 12:49

score 307 · Answer 7 · 2026-03-26 11:01:29

307

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Let $G$ be a finite group, $H\le G$, and $N\unlhd G$. If $|H|=5$ and $|G/N|=7$, prove $H\le N$.

Published on 26 Mar 2026 - 11:01

score 94 · Answer 8 · 2026-03-27 23:20:04

94

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Group of order $3^3$ must have a normal subgroup

Published on 27 Mar 2026 - 23:20

score 1000 · Answer 9 · 2026-03-28 06:10:21

1000

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Let $G$ be a group where $(ab)^3=a^3b^3$ . Prove that $\{ x^3 \mid x \in G \}$ is a normal subgroup of $G$.

Published on 28 Mar 2026 - 6:10

score 83 · Answer 10 · 2020-02-22 09:43:10

83

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For $x\in G$, define $H_x=\{g^{-1}xg \mid g\in G\}$. Under what conditions on $x$ will $H_x \leq G$. Further, if $H_x \leq G$, will $H_x \lhd G$?

Published on 22 Feb 2020 - 9:43

score 93 · Answer 11 · 2020-02-23 16:02:42

93

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Is this true for cosets of normal subgroups?

Published on 23 Feb 2020 - 16:02

score 91 · Answer 12 · 2026-03-27 23:20:00

91

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A group is nilpotent if all of its local subgroups are subnormal

Published on 27 Mar 2026 - 23:20

score 1k · Answer 13 · 2026-03-28 06:06:58

1k

Views

Proving inverse image is a normal subgroup

Published on 28 Mar 2026 - 6:06

score 168 · Answer 14 · 2020-02-26 11:20:02

168

Views

Intuition behind $R$ is a field $\iff$ only ideals are $R$ and $0$

Published on 26 Feb 2020 - 11:20

score 118 · Answer 15 · 2020-02-27 01:06:33

118

Views

Refining a normal series to get a composition series for a group.

Published on 27 Feb 2020 - 1:06

List Question

Question about Reynold's operator of a subgroup

Index of a subgroup in $SL_2(\mathbb{Z})$

Checking a normal subgroup of $S_4$

Proving that subgroup of Rotations in $D_{2n}$ is a normal subgroup

Let $G = \{A \in G L_n(\mathbb{R}) : \mathrm{det} A = 2^k$ for some $k \in Z \}$. Show that $G$ is a normal subgroup of $H = GL_n(\mathbb{R})$.

Proving a property of normal subgroups.

Let $G$ be a finite group, $H\le G$, and $N\unlhd G$. If $|H|=5$ and $|G/N|=7$, prove $H\le N$.

Group of order $3^3$ must have a normal subgroup

Let $G$ be a group where $(ab)^3=a^3b^3$ . Prove that $\{ x^3 \mid x \in G \}$ is a normal subgroup of $G$.

For $x\in G$, define $H_x=\{g^{-1}xg \mid g\in G\}$. Under what conditions on $x$ will $H_x \leq G$. Further, if $H_x \leq G$, will $H_x \lhd G$?

Is this true for cosets of normal subgroups?

A group is nilpotent if all of its local subgroups are subnormal

Proving inverse image is a normal subgroup

Intuition behind $R$ is a field $\iff$ only ideals are $R$ and $0$

Refining a normal series to get a composition series for a group.

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