Question

Show that if N, K are normal subgroups of a group G, and N contains K then we have: $ G / N \cong (G/K) / (N /K) $

score 843 · Answer 1 · 2026-03-25 19:07:11

843

Views

Show that if N, K are normal subgroups of a group G, and N contains K then we have: $ G / N \cong (G/K) / (N /K) $

Published on 25 Mar 2026 - 19:07

score 287 · Answer 2 · 2026-03-27 01:47:00

287

Views

Can a nonabelian group $G$ have a normal abelian subgroup $H$ with $[G:H]=3$?

Published on 27 Mar 2026 - 1:47

score 120 · Answer 3 · 2019-04-26 05:10:31

120

Views

Wikipedia inconsistency with the index 2 subgroups of the Hyperoctahedral group.

Published on 26 Apr 2019 - 5:10

score 359 · Answer 4 · 2026-03-27 01:46:57

359

Views

Are all index 2 subgroups of $(\mathbb{Z} /2\mathbb{Z})^n$ isomorphic to $(\mathbb{Z} /2\mathbb{Z})^{n-1}$

Published on 27 Mar 2026 - 1:46

score 162 · Answer 5 · 2019-04-30 09:11:28

162

Views

How do i show any subgroup of index $p$ is normal?

Published on 30 Apr 2019 - 9:11

score 1.4k · Answer 6 · 2019-05-01 02:09:14

1.4k

Views

Find the normalizer of a cyclic subgroup of $S_7$

Published on 01 May 2019 - 2:09

score 309 · Answer 7 · 2026-03-26 06:21:28

309

Views

Product of all normal subgroups of a group

Published on 26 Mar 2026 - 6:21

score 183 · Answer 8 · 2026-03-25 15:07:25

183

Views

Cosets form a group if normal subgroup

Published on 25 Mar 2026 - 15:07

score 39 · Answer 9 · 2019-05-07 23:07:55

39

Views

A counterexample about inner automorphisms

Published on 07 May 2019 - 23:07

score 1.8k · Answer 10 · 2019-05-08 12:34:15

1.8k

Views

If $G$ be a group of order $8$ and $x$ be a element of order $4$. Prove that $x^2 \in Z(G)$

Published on 08 May 2019 - 12:34

score 459 · Answer 11 · 2019-05-11 12:35:53

459

Views

Find the normal subgroup of matrix group

Published on 11 May 2019 - 12:35

score 68 · Answer 12 · 2019-05-11 14:03:51

68

Views

Prove for a normal subgroup

Published on 11 May 2019 - 14:03

score 69 · Answer 13 · 2019-05-17 23:56:24

69

Views

Why is $\mathbb{Q}[i]$ not a subgroup of $\mathbb{R}$?

Published on 17 May 2019 - 23:56

score 905 · Answer 14 · 2026-03-26 23:10:35

905

Views

let $N_1$, $N_2$ be normal subgroups of group G. Define $f : G → (G/N_1) × (G/N_2)$ by $f(a) = (aN_1, aN_2)$. show f is a homomorfism

Published on 26 Mar 2026 - 23:10

score 129 · Answer 15 · 2019-05-19 12:57:40

129

Views

Prove that $H$ is a system of representatives for the cosets of $N$ in $G$, and that $G/N$ is isomorphic to $H$.

Published on 19 May 2019 - 12:57

List Question

Show that if N, K are normal subgroups of a group G, and N contains K then we have: $ G / N \cong (G/K) / (N /K) $

Can a nonabelian group $G$ have a normal abelian subgroup $H$ with $[G:H]=3$?

Wikipedia inconsistency with the index 2 subgroups of the Hyperoctahedral group.

Are all index 2 subgroups of $(\mathbb{Z} /2\mathbb{Z})^n$ isomorphic to $(\mathbb{Z} /2\mathbb{Z})^{n-1}$

How do i show any subgroup of index $p$ is normal?

Find the normalizer of a cyclic subgroup of $S_7$

Product of all normal subgroups of a group

Cosets form a group if normal subgroup

A counterexample about inner automorphisms

If $G$ be a group of order $8$ and $x$ be a element of order $4$. Prove that $x^2 \in Z(G)$

Find the normal subgroup of matrix group

Prove for a normal subgroup

Why is $\mathbb{Q}[i]$ not a subgroup of $\mathbb{R}$?

let $N_1$, $N_2$ be normal subgroups of group G. Define $f : G → (G/N_1) × (G/N_2)$ by $f(a) = (aN_1, aN_2)$. show f is a homomorfism

Prove that $H$ is a system of representatives for the cosets of $N$ in $G$, and that $G/N$ is isomorphic to $H$.

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