Question

For each $n$ determine whether $S_n$ (1) and $D_n$ (2) are simple or not.

score 274 · Answer 1 · 2026-03-26 01:08:05

274

Views

For each $n$ determine whether $S_n$ (1) and $D_n$ (2) are simple or not.

Published on 26 Mar 2026 - 1:08

score 42 · Answer 2 · 2019-12-12 19:25:48

42

Views

Showing $N_1\times N_2\unlhd G_1\times G_2$ iff there exist $N_1\unlhd G_1$ and $N_2\unlhd G_2$.

Published on 12 Dec 2019 - 19:25

score 41 · Answer 3 · 2019-12-13 05:34:03

41

Views

How to use the property of normal subgroup to show the following

Published on 13 Dec 2019 - 5:34

score 52 · Answer 4 · 2019-12-13 08:32:16

52

Views

Sequence of subgroups of abelian group of cardinality $p^n$

Published on 13 Dec 2019 - 8:32

score 2.3k · Answer 5 · 2019-12-13 10:31:20

2.3k

Views

Normal subgroups of GL$(n,\mathbb{R})$ and SL$(n,\mathbb{R})$

Published on 13 Dec 2019 - 10:31

score 790 · Answer 6 · 2026-03-28 00:49:12

790

Views

If $H$ is a subgroup of $G$ and contains all commutators $aba^{-1}b^{-1}$ with $a, b \in G$, then $H$ is normal.

Published on 28 Mar 2026 - 0:49

score 95 · Answer 7 · 2026-03-25 22:10:12

95

Views

Normal Subgroups of Solvable Groups with elementary abelian Sylow 2 subgroup

Published on 25 Mar 2026 - 22:10

score 196 · Answer 8 · 2026-03-26 22:14:13

196

Views

Preimage of cosets under a surjective homomorphism

Published on 26 Mar 2026 - 22:14

score 286 · Answer 9 · 2026-03-28 15:21:30

286

Views

Prove that if $H$ is a normal subgroup in $S_n$, and $H$ contains a $2$ cycle, then $H = S_n.$

Published on 28 Mar 2026 - 15:21

score 868 · Answer 10 · 2019-12-22 05:57:04

868

Views

What is the difference between left- and right-conjugation in a group?

Published on 22 Dec 2019 - 5:57

score 583 · Answer 11 · 2026-03-28 00:54:11

583

Views

Homomorphism to abelian group

Published on 28 Mar 2026 - 0:54

score 89 · Answer 12 · 2019-12-22 09:09:37

89

Views

If $\forall x \in G, \exists k \in \mathbb Z^+ \backepsilon xa=a^kx $, then $\langle a \rangle$ is a normal subgroup

Published on 22 Dec 2019 - 9:09

score 34 · Answer 13 · 2019-12-24 06:59:43

34

Views

Two subgroups of the same order, and the normaliser of one in the other

Published on 24 Dec 2019 - 6:59

score 109 · Answer 14 · 2019-12-25 21:42:00

109

Views

Dummit and Foote 4.2 Corollary 5. Group action

Published on 25 Dec 2019 - 21:42

score 92 · Answer 15 · 2026-03-26 01:14:48

92

Views

Problem from Galois' personal works

Published on 26 Mar 2026 - 1:14

List Question

For each $n$ determine whether $S_n$ (1) and $D_n$ (2) are simple or not.

Showing $N_1\times N_2\unlhd G_1\times G_2$ iff there exist $N_1\unlhd G_1$ and $N_2\unlhd G_2$.

How to use the property of normal subgroup to show the following

Sequence of subgroups of abelian group of cardinality $p^n$

Normal subgroups of GL$(n,\mathbb{R})$ and SL$(n,\mathbb{R})$

If $H$ is a subgroup of $G$ and contains all commutators $aba^{-1}b^{-1}$ with $a, b \in G$, then $H$ is normal.

Normal Subgroups of Solvable Groups with elementary abelian Sylow 2 subgroup

Preimage of cosets under a surjective homomorphism

Prove that if $H$ is a normal subgroup in $S_n$, and $H$ contains a $2$ cycle, then $H = S_n.$

What is the difference between left- and right-conjugation in a group?

Homomorphism to abelian group

If $\forall x \in G, \exists k \in \mathbb Z^+ \backepsilon xa=a^kx $, then $\langle a \rangle$ is a normal subgroup

Two subgroups of the same order, and the normaliser of one in the other

Dummit and Foote 4.2 Corollary 5. Group action

Problem from Galois' personal works

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