Question

Let $G = \langle A,B,C,D\rangle$. If $\langle X,Y\rangle$ is free of rank $2$ for every $X\neq Y,X,Y\in \{A,B,C,D\}$, is $G$ free of rank $4$?

score 124 · Answer 1 · 2026-03-26 00:53:55

124

Views

Let $G = \langle A,B,C,D\rangle$. If $\langle X,Y\rangle$ is free of rank $2$ for every $X\neq Y,X,Y\in \{A,B,C,D\}$, is $G$ free of rank $4$?

Published on 26 Mar 2026 - 0:53

score 311 · Answer 2 · 2026-03-26 00:52:58

311

Views

One missing step in proving $\mathbb{Z}\times \mathbb{Z} \cong \langle a,b\,|\, [a,b]=1\rangle$

Published on 26 Mar 2026 - 0:52

score 114 · Answer 3 · 2026-03-26 09:49:51

114

Views

A free abelian group and a free group quotient by its commutator group

Published on 26 Mar 2026 - 9:49

score 223 · Answer 4 · 2026-03-26 04:33:11

223

Views

Applications of Tits' alternative in number theory

Published on 26 Mar 2026 - 4:33

score 135 · Answer 5 · 2026-03-26 04:20:01

135

Views

Let $G$ be a group with a free subgroup of rank $2$. Let $H\leq G$ be such that $[G:H]<\infty$. Then $H$ also contains a free subgroup of rank $2$.

Published on 26 Mar 2026 - 4:20

score 104 · Answer 6 · 2026-03-26 12:37:06

104

Views

Does $F/N_{1}\cong F/N_{2}$ implies $N_{1}\cong N_{2}$ and vice versa?

Published on 26 Mar 2026 - 12:37

score 179 · Answer 7 · 2026-03-22 10:23:17

179

Views

Are the terms of the derived series of finitely generated groups finitely normally generated?

Published on 22 Mar 2026 - 10:23

score 171 · Answer 8 · 2016-07-08 15:03:24

171

Views

solve a specific word problem in free groups

Published on 08 Jul 2016 - 15:03

score 331 · Answer 9 · 2016-07-10 06:52:39

331

Views

About Structure of Free Algebra over $K$

Published on 10 Jul 2016 - 6:52

score 571 · Answer 10 · 2016-07-11 04:48:56

571

Views

What is significance of this proof of existence of free groups (Lang's Algebra)

Published on 11 Jul 2016 - 4:48

score 92 · Answer 11 · 2016-07-11 04:59:50

92

Views

On a property of generating set for groups

Published on 11 Jul 2016 - 4:59

score 223 · Answer 12 · 2026-03-26 04:30:11

223

Views

Are Free Groups the "Smallest Group" Containing their Generators

Published on 26 Mar 2026 - 4:30

score 90 · Answer 13 · 2016-07-12 06:11:38

90

Views

Formal construction of free groups and objections in arguments

Published on 12 Jul 2016 - 6:11

score 79 · Answer 14 · 2016-07-13 10:44:26

79

Views

Problem in understanding some steps in proof

Published on 13 Jul 2016 - 10:44

score 513 · Answer 15 · 2016-07-15 18:45:01

513

Views

To prove: The intersection of all normal subgroups of finite index of a free group is trivial.

Published on 15 Jul 2016 - 18:45

List Question

Let $G = \langle A,B,C,D\rangle$. If $\langle X,Y\rangle$ is free of rank $2$ for every $X\neq Y,X,Y\in \{A,B,C,D\}$, is $G$ free of rank $4$?

One missing step in proving $\mathbb{Z}\times \mathbb{Z} \cong \langle a,b\,|\, [a,b]=1\rangle$

A free abelian group and a free group quotient by its commutator group

Applications of Tits' alternative in number theory

Let $G$ be a group with a free subgroup of rank $2$. Let $H\leq G$ be such that $[G:H]<\infty$. Then $H$ also contains a free subgroup of rank $2$.

Does $F/N_{1}\cong F/N_{2}$ implies $N_{1}\cong N_{2}$ and vice versa?

Are the terms of the derived series of finitely generated groups finitely normally generated?

solve a specific word problem in free groups

About Structure of Free Algebra over $K$

What is significance of this proof of existence of free groups (Lang's Algebra)

On a property of generating set for groups

Are Free Groups the "Smallest Group" Containing their Generators

Formal construction of free groups and objections in arguments

Problem in understanding some steps in proof

To prove: The intersection of all normal subgroups of finite index of a free group is trivial.

Trending Questions

Popular # Hahtags

Popular Questions