Question

Normal Subgroups and Quotient Groups help

score 34 · Answer 1 · 2026-03-25 14:28:51

34

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Normal Subgroups and Quotient Groups help

Published on 25 Mar 2026 - 14:28

score 161 · Answer 2 · 2019-01-15 17:58:21

161

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Finding a normal subgroup in $G := GL_2( \mathbb F_7)$

Published on 15 Jan 2019 - 17:58

score 111 · Answer 3 · 2026-03-25 22:05:42

111

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Show that a finite generated subgroup $H$ of $G$ with index 3 exists which is not normal in $G$.

Published on 25 Mar 2026 - 22:05

score 260 · Answer 4 · 2026-03-26 09:48:33

260

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Normal subgroup and corresponding homomorphism

Published on 26 Mar 2026 - 9:48

score 88 · Answer 5 · 2019-01-19 20:13:06

88

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Order of elements from coset and Schur-Zassenhaus Theorem (Exercise $3.B.6$ FGT)

Published on 19 Jan 2019 - 20:13

score 184 · Answer 6 · 2026-03-26 12:15:34

184

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Prove or disprove. Let $G$ be an abelian group. Let $N \triangleleft G$. Then, $ G\cong N \times G/N. $

Published on 26 Mar 2026 - 12:15

score 195 · Answer 7 · 2019-01-22 20:50:32

195

Views

multiplying two normal subgroups is still normal?

Published on 22 Jan 2019 - 20:50

score 76 · Answer 8 · 2026-03-19 23:50:36

76

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Characteristic subgroups and factorization

Published on 19 Mar 2026 - 23:50

score 3.6k · Answer 9 · 2019-01-27 05:56:27

3.6k

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If $H$ is a subgroup, and $xHx^{-1} \subsetneq H$, for all $x$ in $G$, then is H a normal subgroup?

Published on 27 Jan 2019 - 5:56

score 51 · Answer 10 · 2019-01-27 13:29:44

51

Views

Groups and normal subgroups

Published on 27 Jan 2019 - 13:29

score 989 · Answer 11 · 2019-01-28 07:55:48

989

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If N is a normal subgroup of a group G, then prove that G/N is a group with respect to multiplication of cosets.

Published on 28 Jan 2019 - 7:55

score 155 · Answer 12 · 2019-01-31 16:43:19

155

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The groups $G_1, G_2$ and the normal subgroups $N_1,N_2$ are isomorphic. Dis/prove $G_1/N_1\cong G_2/N_2$

Published on 31 Jan 2019 - 16:43

score 50 · Answer 13 · 2026-03-26 13:52:13

50

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How do the elements of $(G\times G) /D$ look like? $D:=\{(g,g)\in G\times G\}$ and $G$ is abelian

Published on 26 Mar 2026 - 13:52

score 598 · Answer 14 · 2026-03-26 14:34:45

598

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Excercise with the normal subgroup $K$ of $G$ with $K:=\bigcap\{H \text{ subgroup of } G: \forall_{x,y\in G}:xyx^{-1}y^{-1}\in H\}$

Published on 26 Mar 2026 - 14:34

score 110 · Answer 15 · 2026-03-26 03:01:34

110

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Property of Sylow $2$-subgroups of $S_n$ and $S_{n+1}$

Published on 26 Mar 2026 - 3:01

List Question

Normal Subgroups and Quotient Groups help

Finding a normal subgroup in $G := GL_2( \mathbb F_7)$

Show that a finite generated subgroup $H$ of $G$ with index 3 exists which is not normal in $G$.

Normal subgroup and corresponding homomorphism

Order of elements from coset and Schur-Zassenhaus Theorem (Exercise $3.B.6$ FGT)

Prove or disprove. Let $G$ be an abelian group. Let $N \triangleleft G$. Then, $ G\cong N \times G/N. $

multiplying two normal subgroups is still normal?

Characteristic subgroups and factorization

If $H$ is a subgroup, and $xHx^{-1} \subsetneq H$, for all $x$ in $G$, then is H a normal subgroup?

Groups and normal subgroups

If N is a normal subgroup of a group G, then prove that G/N is a group with respect to multiplication of cosets.

The groups $G_1, G_2$ and the normal subgroups $N_1,N_2$ are isomorphic. Dis/prove $G_1/N_1\cong G_2/N_2$

How do the elements of $(G\times G) /D$ look like? $D:=\{(g,g)\in G\times G\}$ and $G$ is abelian

Excercise with the normal subgroup $K$ of $G$ with $K:=\bigcap\{H \text{ subgroup of } G: \forall_{x,y\in G}:xyx^{-1}y^{-1}\in H\}$

Property of Sylow $2$-subgroups of $S_n$ and $S_{n+1}$

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