Question

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

score 274 · Answer 1 · 2026-04-16 11:49:48

274

Views

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

Published on 16 Apr 2026 - 11:49

score 679 · Answer 2 · 2026-04-12 09:16:02

679

Views

Is union of any number conjugacy classes is subgroup?

Published on 12 Apr 2026 - 9:16

score 1.8k · Answer 3 · 2026-04-11 20:21:12

1.8k

Views

Embedding of a subgroup into a group

Published on 11 Apr 2026 - 20:21

score 93 · Answer 4 · 2026-04-16 09:55:26

93

Views

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

Published on 16 Apr 2026 - 9:55

score 82 · Answer 5 · 2026-04-14 21:28:30

82

Views

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

Published on 14 Apr 2026 - 21:28

score 361 · Answer 6 · 2026-04-10 09:34:58

361

Views

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

Published on 10 Apr 2026 - 9:34

score 637 · Answer 7 · 2026-04-14 17:22:34

637

Views

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

Published on 14 Apr 2026 - 17:22

score 92 · Answer 8 · 2026-05-10 14:32:36

92

Views

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

Published on 10 May 2026 - 14:32

score 68 · Answer 9 · 2026-05-10 16:06:22

68

Views

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

Published on 10 May 2026 - 16:06

score 256 · Answer 10 · 2026-04-13 15:15:31

256

Views

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

Published on 13 Apr 2026 - 15:15

score 870 · Answer 11 · 2026-04-17 10:54:45

870

Views

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

Published on 17 Apr 2026 - 10:54

score 95 · Answer 12 · 2026-04-16 02:15:20

95

Views

normal subgroup, diagonal embedding.

Published on 16 Apr 2026 - 2:15

score 64 · Answer 13 · 2026-05-10 15:14:05

64

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 10 May 2026 - 15:14

score 41 · Answer 14 · 2026-04-12 21:41:44

41

Views

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

Published on 12 Apr 2026 - 21:41

score 759 · Answer 15 · 2026-04-16 00:30:37

759

Views

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

Published on 16 Apr 2026 - 0:30

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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