Question

Torsion-free abelian groups of finite rank and a subgroup of finite index (Fuchs' problem) - self study

score 170 · Answer 1 · 2026-04-15 04:49:53

170

Views

Torsion-free abelian groups of finite rank and a subgroup of finite index (Fuchs' problem) - self study

Published on 15 Apr 2026 - 4:49

score 212 · Answer 2 · 2026-04-12 04:41:28

212

Views

Are infinite indexes multiplicative?

Published on 12 Apr 2026 - 4:41

score 311 · Answer 3 · 2026-04-12 20:13:33

311

Views

Is there a group $G$ and subgroup $H$, such that there exists $g\in G$ with $gHg^{-1} \subset H$ and $|H:gHg^{-1}|$ is infinite?

Published on 12 Apr 2026 - 20:13

score 211 · Answer 4 · 2026-04-11 03:11:17

211

Views

Is $Z(\Sigma) \cong E$?

Published on 11 Apr 2026 - 3:11

score 721 · Answer 5 · 2026-05-10 14:36:15

721

Views

Is the free product of residually finite groups always residually finite?

Published on 10 May 2026 - 14:36

score 338 · Answer 6 · 2026-04-14 13:56:55

338

Views

Let G be a group with composition series. Let $H\triangleleft G$. Then $H$ is in some of the series.

Published on 14 Apr 2026 - 13:56

score 443 · Answer 7 · 2026-04-15 08:42:33

443

Views

The number of elements not in conjugate of a subgroup

Published on 15 Apr 2026 - 8:42

score 76 · Answer 8 · 2026-04-13 16:21:47

76

Views

Correcting Proof of Lemma 10 in Kaplansky's Infinite Abelian Groups

Published on 13 Apr 2026 - 16:21

score 46 · Answer 9 · 2026-04-15 05:21:38

46

Views

Subgroup of non-simple group necessarily non-simple?

Published on 15 Apr 2026 - 5:21

score 81 · Answer 10 · 2026-04-25 15:27:27

81

Views

Does there exist a verbally simple group, which is not characteristically simple?

Published on 25 Apr 2026 - 15:27

score 70 · Answer 11 · 2026-04-15 06:25:08

70

Views

Infinite Abelian Groups: Unnecessary Hypothesis in Kaplansky's Lemma 7

Published on 15 Apr 2026 - 6:25

score 72 · Answer 12 · 2026-04-25 11:48:35

72

Views

Does there exist an Artinian verbally simple group, which is not characteristically simple?

Published on 25 Apr 2026 - 11:48

score 433 · Answer 13 · 2026-04-11 05:30:42

433

Views

Finitely generated, non abelian, infinite group

Published on 11 Apr 2026 - 5:30

score 64 · Answer 14 · 2026-04-14 16:04:55

64

Views

Does there exist an infinite non-abelian group, such that all its nontrivial proper subgroups are isomorphic to $C_\infty$?

Published on 14 Apr 2026 - 16:04

score 404 · Answer 15 · 2026-04-15 00:58:05

404

Views

Is there some sort of classification of all minimal non-cyclic groups?

Published on 15 Apr 2026 - 0:58

List Question

Torsion-free abelian groups of finite rank and a subgroup of finite index (Fuchs' problem) - self study

Are infinite indexes multiplicative?

Is there a group $G$ and subgroup $H$, such that there exists $g\in G$ with $gHg^{-1} \subset H$ and $|H:gHg^{-1}|$ is infinite?

Is $Z(\Sigma) \cong E$?

Is the free product of residually finite groups always residually finite?

Let G be a group with composition series. Let $H\triangleleft G$. Then $H$ is in some of the series.

The number of elements not in conjugate of a subgroup

Correcting Proof of Lemma 10 in Kaplansky's Infinite Abelian Groups

Subgroup of non-simple group necessarily non-simple?

Does there exist a verbally simple group, which is not characteristically simple?

Infinite Abelian Groups: Unnecessary Hypothesis in Kaplansky's Lemma 7

Does there exist an Artinian verbally simple group, which is not characteristically simple?

Finitely generated, non abelian, infinite group

Does there exist an infinite non-abelian group, such that all its nontrivial proper subgroups are isomorphic to $C_\infty$?

Is there some sort of classification of all minimal non-cyclic groups?

Trending Questions

Popular # Hahtags

Popular Questions