Question

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

score 167 · Answer 1 · 2019-01-29 19:50:48

167

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

Published on 29 Jan 2019 - 19:50

score 209 · Answer 2 · 2019-02-04 10:24:42

209

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Are infinite indexes multiplicative?

Published on 04 Feb 2019 - 10:24

score 308 · Answer 3 · 2019-02-21 10:32:34

308

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 21 Feb 2019 - 10:32

score 207 · Answer 4 · 2019-03-02 16:46:36

207

Views

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

Published on 02 Mar 2019 - 16:46

score 717 · Answer 5 · 2019-03-12 17:18:46

717

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

Published on 12 Mar 2019 - 17:18

score 335 · Answer 6 · 2019-03-13 15:00:40

335

Views

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

Published on 13 Mar 2019 - 15:00

score 441 · Answer 7 · 2019-03-16 17:56:04

441

Views

The number of elements not in conjugate of a subgroup

Published on 16 Mar 2019 - 17:56

score 73 · Answer 8 · 2019-03-17 12:39:17

73

Views

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

Published on 17 Mar 2019 - 12:39

score 44 · Answer 9 · 2019-03-19 12:37:57

44

Views

Subgroup of non-simple group necessarily non-simple?

Published on 19 Mar 2019 - 12:37

score 77 · Answer 10 · 2026-03-19 15:49:50

77

Views

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

Published on 19 Mar 2026 - 15:49

score 67 · Answer 11 · 2019-03-22 13:10:22

67

Views

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

Published on 22 Mar 2019 - 13:10

score 68 · Answer 12 · 2026-03-19 15:15:17

68

Views

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

Published on 19 Mar 2026 - 15:15

score 430 · Answer 13 · 2019-04-09 11:11:29

430

Views

Finitely generated, non abelian, infinite group

Published on 09 Apr 2019 - 11:11

score 61 · Answer 14 · 2019-04-12 12:07:38

61

Views

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

Published on 12 Apr 2019 - 12:07

score 401 · Answer 15 · 2019-05-01 21:07:34

401

Views

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

Published on 01 May 2019 - 21:07

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?

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