Question

A normal subgroup of the commutator subgroup (G,G) is normal in G

score 271 · Answer 1 · 2018-06-03 13:57:09

271

Views

A normal subgroup of the commutator subgroup (G,G) is normal in G

Published on 03 Jun 2018 - 13:57

score 676 · Answer 2 · 2018-06-12 04:11:59

676

Views

Is union of any number conjugacy classes is subgroup?

Published on 12 Jun 2018 - 4:11

score 1.8k · Answer 3 · 2018-06-13 00:26:01

1.8k

Views

Embedding of a subgroup into a group

Published on 13 Jun 2018 - 0:26

score 90 · Answer 4 · 2018-06-14 13:13:33

90

Views

Suppose $H\triangleleft G$ and $n=[G:H]<\infty$. Prove $\forall_{g\in G}:g^n\in H$ .

Published on 14 Jun 2018 - 13:13

score 81 · Answer 5 · 2026-03-25 16:08:20

81

Views

Find a homomorphism $f$ such that $\ker f = N$, a normal subgroup.

Published on 25 Mar 2026 - 16:08

score 359 · Answer 6 · 2026-03-25 12:24:18

359

Views

Prove that $H\cap gHg^{-1}$ is normal

Published on 25 Mar 2026 - 12:24

score 634 · Answer 7 · 2018-06-19 18:32:47

634

Views

Subgroups of the additive group of the remainders mod 8 $(\mathbb{Z}_8, \underline{+}$

Published on 19 Jun 2018 - 18:32

score 89 · Answer 8 · 2026-03-25 09:49:58

89

Views

Normal subgroup of a normal subgroup of a group is not always a normal subgroup of a group. Prove using GAP.

Published on 25 Mar 2026 - 9:49

score 65 · Answer 9 · 2026-03-25 16:02:12

65

Views

If a group and its quotient group are isomorphic, the normal subgroup only has identity element?

Published on 25 Mar 2026 - 16:02

score 253 · Answer 10 · 2018-07-03 00:42:54

253

Views

Given a subgroup of $GL_2(\mathbb C)$ generated by two elements, prove that all its subgroups are normal

Published on 03 Jul 2018 - 0:42

score 868 · Answer 11 · 2026-03-25 06:06:45

868

Views

If $P$ or $Q$ is normal then both $P$ and $Q$ are characteristic in $PQ$

Published on 25 Mar 2026 - 6:06

score 92 · Answer 12 · 2018-07-07 14:31:48

92

Views

normal subgroup, diagonal embedding.

Published on 07 Jul 2018 - 14:31

score 63 · Answer 13 · 2026-03-25 01:17:07

63

Views

Is there a way to evaluate $\min\{k |\forall A \subset G \text{ if }|A| > k\text{, then } AAA = \langle A \rangle \}$?

Published on 25 Mar 2026 - 1:17

score 38 · Answer 14 · 2018-07-19 15:36:19

38

Views

When we can conclude that $H^{\pi}$ equals the normal closure of $H$ in $G$?

Published on 19 Jul 2018 - 15:36

score 758 · Answer 15 · 2026-03-25 04:43:05

758

Views

Are there any natural numbers $n$ that satisfy the condition $7921\sigma(n) = 15840n$?

Published on 25 Mar 2026 - 4:43

List Question

A normal subgroup of the commutator subgroup (G,G) is normal in G

Is union of any number conjugacy classes is subgroup?

Embedding of a subgroup into a group

Suppose $H\triangleleft G$ and $n=[G:H]<\infty$. Prove $\forall_{g\in G}:g^n\in H$ .

Find a homomorphism $f$ such that $\ker f = N$, a normal subgroup.

Prove that $H\cap gHg^{-1}$ is normal

Subgroups of the additive group of the remainders mod 8 $(\mathbb{Z}_8, \underline{+}$

Normal subgroup of a normal subgroup of a group is not always a normal subgroup of a group. Prove using GAP.

If a group and its quotient group are isomorphic, the normal subgroup only has identity element?

Given a subgroup of $GL_2(\mathbb C)$ generated by two elements, prove that all its subgroups are normal

If $P$ or $Q$ is normal then both $P$ and $Q$ are characteristic in $PQ$

normal subgroup, diagonal embedding.

Is there a way to evaluate $\min\{k |\forall A \subset G \text{ if }|A| > k\text{, then } AAA = \langle A \rangle \}$?

When we can conclude that $H^{\pi}$ equals the normal closure of $H$ in $G$?

Are there any natural numbers $n$ that satisfy the condition $7921\sigma(n) = 15840n$?

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