Question

$G$ be an infinite group such that $|Aut (G)|=2$ , then is $G$ cyclic ?

score 620 · Answer 1 · 2016-04-30 06:01:22

620

Views

$G$ be an infinite group such that $|Aut (G)|=2$ , then is $G$ cyclic ?

Published on 30 Apr 2016 - 6:01

score 221 · Answer 2 · 2016-04-30 07:58:21

221

Views

$G$ is an infinite abelian group such that $G \cong H$ for every non trivial subgroup $H$ of $G$ , then is $G$ cyclic?

Published on 30 Apr 2016 - 7:58

score 98 · Answer 3 · 2016-05-06 18:40:29

98

Views

Subsets of $G$-sets with sharply transitive $G$-action

Published on 06 May 2016 - 18:40

score 245 · Answer 4 · 2016-05-22 17:27:42

245

Views

isomorphic subgroups of the additive group of rational numbers

Published on 22 May 2016 - 17:27

score 2.4k · Answer 5 · 2016-05-28 03:26:34

2.4k

Views

Finding subgroups of the Real Numbers

Published on 28 May 2016 - 3:26

score 2.8k · Answer 6 · 2016-06-03 14:10:10

2.8k

Views

Infinite non abelian group with finite order elements

Published on 03 Jun 2016 - 14:10

score 88 · Answer 7 · 2016-06-15 11:57:38

88

Views

Does there exist $A$ of infinite order in $\{ A \in GL_2(\mathbb{R}) : A^T = A^{-1} \}$?

Published on 15 Jun 2016 - 11:57

score 171 · Answer 8 · 2016-06-19 10:19:31

171

Views

Does there exist any infinite group $G$ where each element is of order $2$?

Published on 19 Jun 2016 - 10:19

score 429 · Answer 9 · 2016-07-03 05:30:11

429

Views

Are the groups $\mathbb C^\times \times \mathbb R^ \times$ and $\mathbb R^ \times\times \mathbb R^ \times$ isomorphic?

Published on 03 Jul 2016 - 5:30

score 159 · Answer 10 · 2016-07-03 06:45:55

159

Views

Are the groups $\mathbb R/ \mathbb Z $ and $ \mathbb R^2 / (\mathbb Z \times \{0\} )$ isomorphic?

Published on 03 Jul 2016 - 6:45

score 2.5k · Answer 11 · 2013-06-13 06:39:22

2.5k

Views

Does every infinite group have a maximal subgroup?

Published on 13 Jun 2013 - 6:39

score 1k · Answer 12 · 2013-06-18 04:07:57

1k

Views

If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?

Published on 18 Jun 2013 - 4:07

score 475 · Answer 13 · 2026-03-26 23:49:18

475

Views

Classify all groups containing isomorphic copy of $\mathbb{Z}$ of index $2$.

Published on 26 Mar 2026 - 23:49

score 90 · Answer 14 · 2013-07-26 01:47:41

90

Views

How to directly prove an identity on infinite series

Published on 26 Jul 2013 - 1:47

score 116 · Answer 15 · 2013-08-04 19:11:33

116

Views

Problem on non abelian tensor product of groups

Published on 04 Aug 2013 - 19:11

List Question

$G$ be an infinite group such that $|Aut (G)|=2$ , then is $G$ cyclic ?

$G$ is an infinite abelian group such that $G \cong H$ for every non trivial subgroup $H$ of $G$ , then is $G$ cyclic?

Subsets of $G$-sets with sharply transitive $G$-action

isomorphic subgroups of the additive group of rational numbers

Finding subgroups of the Real Numbers

Infinite non abelian group with finite order elements

Does there exist $A$ of infinite order in $\{ A \in GL_2(\mathbb{R}) : A^T = A^{-1} \}$?

Does there exist any infinite group $G$ where each element is of order $2$?

Are the groups $\mathbb C^\times \times \mathbb R^ \times$ and $\mathbb R^ \times\times \mathbb R^ \times$ isomorphic?

Are the groups $\mathbb R/ \mathbb Z $ and $ \mathbb R^2 / (\mathbb Z \times \{0\} )$ isomorphic?

Does every infinite group have a maximal subgroup?

If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?

Classify all groups containing isomorphic copy of $\mathbb{Z}$ of index $2$.

How to directly prove an identity on infinite series

Problem on non abelian tensor product of groups

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