Question

Showing that $H'$ is a normal subgroup of $G'$

score 43 · Answer 1 · 2016-10-09 12:53:44

43

Views

Showing that $H'$ is a normal subgroup of $G'$

Published on 09 Oct 2016 - 12:53

score 115 · Answer 2 · 2016-10-09 16:27:08

115

Views

Showing it is a normal subgroup

Published on 09 Oct 2016 - 16:27

score 20 · Answer 3 · 2016-10-10 02:07:37

20

Views

Calculating the index of an aditive subgroup.

Published on 10 Oct 2016 - 2:07

score 150 · Answer 4 · 2016-10-10 04:37:11

150

Views

Normal Subgroups, quotient groups

Published on 10 Oct 2016 - 4:37

score 81 · Answer 5 · 2016-10-10 21:53:13

81

Views

Union of finite subgroups not necessarily normal?

Published on 10 Oct 2016 - 21:53

score 2k · Answer 6 · 2016-10-11 21:04:04

2k

Views

Let G be a finite group with p be the smallest prime divisor of $| G|.$ Then every subgroup H of index p in G is normal in G .

Published on 11 Oct 2016 - 21:04

score 274 · Answer 7 · 2026-03-26 22:53:24

274

Views

$H$ is a normal subgroup of $D_8$

Published on 26 Mar 2026 - 22:53

score 211 · Answer 8 · 2016-10-17 11:57:01

211

Views

If $H \leqslant G$, $N \trianglelefteq G$, why does $HN=NH$ imply $HN \subseteq \langle H,N \rangle$?

Published on 17 Oct 2016 - 11:57

score 135 · Answer 9 · 2016-10-17 12:24:45

135

Views

For $x,y \in \mathbb{Q}\setminus\{ 0\}$, prove that $\mathbb{Q}/\langle x \rangle \simeq \mathbb{Q}/ \langle y \rangle$.

Published on 17 Oct 2016 - 12:24

score 40 · Answer 10 · 2026-03-30 09:47:31

40

Views

Is this condition equivalent to normality (as a subgroup)?

Published on 30 Mar 2026 - 9:47

score 538 · Answer 11 · 2016-10-21 16:26:21

538

Views

Example of A, B, G such that A is a normal subgroup of B, B is a normal subgroup of G, but A is not a normal subgroup of G

Published on 21 Oct 2016 - 16:26

score 52 · Answer 12 · 2016-10-22 23:35:41

52

Views

Finding all quotient groups $F/N$ up to isomorphism where $N \leqslant F \leqslant \langle H, N \rangle$.

Published on 22 Oct 2016 - 23:35

score 58 · Answer 13 · 2026-03-30 05:02:13

58

Views

Show that $\{1, (1\quad3)(2\quad4), (1\quad4)(2\quad3),(1\quad2)(3\quad4)\}$ is a normal subgroup of $\mathrm{S}_4$

Published on 30 Mar 2026 - 5:02

score 7.8k · Answer 14 · 2026-03-30 04:59:07

7.8k

Views

Prove that $A_n$ is a Normal subgroup of $S_n$?

Published on 30 Mar 2026 - 4:59

score 179 · Answer 15 · 2016-11-03 16:16:38

179

Views

A normal subgroup $H$ of $G$, $[G:H] = n$

Published on 03 Nov 2016 - 16:16

List Question

Showing that $H'$ is a normal subgroup of $G'$

Showing it is a normal subgroup

Calculating the index of an aditive subgroup.

Normal Subgroups, quotient groups

Union of finite subgroups not necessarily normal?

Let G be a finite group with p be the smallest prime divisor of $| G|.$ Then every subgroup H of index p in G is normal in G .

$H$ is a normal subgroup of $D_8$

If $H \leqslant G$, $N \trianglelefteq G$, why does $HN=NH$ imply $HN \subseteq \langle H,N \rangle$?

For $x,y \in \mathbb{Q}\setminus\{ 0\}$, prove that $\mathbb{Q}/\langle x \rangle \simeq \mathbb{Q}/ \langle y \rangle$.

Is this condition equivalent to normality (as a subgroup)?

Example of A, B, G such that A is a normal subgroup of B, B is a normal subgroup of G, but A is not a normal subgroup of G

Finding all quotient groups $F/N$ up to isomorphism where $N \leqslant F \leqslant \langle H, N \rangle$.

Show that $\{1, (1\quad3)(2\quad4), (1\quad4)(2\quad3),(1\quad2)(3\quad4)\}$ is a normal subgroup of $\mathrm{S}_4$

Prove that $A_n$ is a Normal subgroup of $S_n$?

A normal subgroup $H$ of $G$, $[G:H] = n$

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