Question

Rank of the subgroup of a free group may be much greater than the rank of the whole group

score 592 · Answer 1 · 2017-06-01 11:07:02

592

Views

Rank of the subgroup of a free group may be much greater than the rank of the whole group

Published on 01 Jun 2017 - 11:07

score 4.5k · Answer 2 · 2017-06-01 11:33:30

4.5k

Views

Why is "A free group on more than one generator is not abelian." true?

Published on 01 Jun 2017 - 11:33

score 56 · Answer 3 · 2017-06-01 13:52:26

56

Views

Some arguments on free groups that I couldn't understand

Published on 01 Jun 2017 - 13:52

score 2.1k · Answer 4 · 2017-06-05 09:20:18

2.1k

Views

Why is the fundamental group of torus with finitely many points removed a bouquet of circles?

Published on 05 Jun 2017 - 9:20

score 33 · Answer 5 · 2026-03-27 20:21:03

33

Views

$G=\langle S|R\rangle$ is finitely presented simple, then if $w\neq e$ in $G$, $\langle\langle w\cup R \rangle\rangle = F(S)$

Published on 27 Mar 2026 - 20:21

score 135 · Answer 6 · 2026-03-28 04:34:10

135

Views

Free monoids in Milne's Group Theory

Published on 28 Mar 2026 - 4:34

score 230 · Answer 7 · 2026-03-28 21:06:49

230

Views

How can I tell if elements generate or $F_n$ or $F_n \times F_n$?

Published on 28 Mar 2026 - 21:06

score 283 · Answer 8 · 2026-03-26 17:53:22

283

Views

Understanding statement: F free of rank r $\Rightarrow$ F/F' free abelian of rank r

Published on 26 Mar 2026 - 17:53

score 62 · Answer 9 · 2017-06-29 06:57:57

62

Views

Well definedness of a map defined on a set of generators of a group G.

Published on 29 Jun 2017 - 6:57

score 39 · Answer 10 · 2026-03-28 00:06:03

39

Views

Notation and definition on book Presentations of Groups

Published on 28 Mar 2026 - 0:06

score 104 · Answer 11 · 2017-07-07 10:53:22

104

Views

Jacobson's proof of $D_n = \langle x,y\mid x^n=y^2=1, (xy)^2 = 1\rangle$

Published on 07 Jul 2017 - 10:53

score 392 · Answer 12 · 2017-07-07 16:26:10

392

Views

Presentation of the group $\mathbb Z^3$ with a special product (how to complete the proof?)

Published on 07 Jul 2017 - 16:26

score 78 · Answer 13 · 2017-07-13 11:57:58

78

Views

Reference request: fundamental groups

Published on 13 Jul 2017 - 11:57

score 202 · Answer 14 · 2017-07-18 22:40:41

202

Views

Question Regarding Equivalence of Definitions of Homomorphisms of Groups

Published on 18 Jul 2017 - 22:40

score 195 · Answer 15 · 2017-07-24 16:52:20

195

Views

A question about the free resolution of an abelian group.

Published on 24 Jul 2017 - 16:52

List Question

Rank of the subgroup of a free group may be much greater than the rank of the whole group

Why is "A free group on more than one generator is not abelian." true?

Some arguments on free groups that I couldn't understand

Why is the fundamental group of torus with finitely many points removed a bouquet of circles?

$G=\langle S|R\rangle$ is finitely presented simple, then if $w\neq e$ in $G$, $\langle\langle w\cup R \rangle\rangle = F(S)$

Free monoids in Milne's Group Theory

How can I tell if elements generate or $F_n$ or $F_n \times F_n$?

Understanding statement: F free of rank r $\Rightarrow$ F/F' free abelian of rank r

Well definedness of a map defined on a set of generators of a group G.

Notation and definition on book Presentations of Groups

Jacobson's proof of $D_n = \langle x,y\mid x^n=y^2=1, (xy)^2 = 1\rangle$

Presentation of the group $\mathbb Z^3$ with a special product (how to complete the proof?)

Reference request: fundamental groups

Question Regarding Equivalence of Definitions of Homomorphisms of Groups

A question about the free resolution of an abelian group.

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