Question

If $F$ is free with basis $X$ and if $F'$ is the commutator subgroup of $F$, then $F/F'$ is free abelian with basis all cosets $xF'$ with $x \in X$

score 76 · Answer 1 · 2017-07-25 14:12:16

76

Views

If $F$ is free with basis $X$ and if $F'$ is the commutator subgroup of $F$, then $F/F'$ is free abelian with basis all cosets $xF'$ with $x \in X$

Published on 25 Jul 2017 - 14:12

score 7.6k · Answer 2 · 2017-07-25 15:10:27

7.6k

Views

What is a simple example of a free group?

Published on 25 Jul 2017 - 15:10

score 71 · Answer 3 · 2026-03-27 13:20:00

71

Views

Did the author switch notation in a proof and redefine things?

Published on 27 Mar 2026 - 13:20

score 265 · Answer 4 · 2026-03-28 08:09:36

265

Views

Free monoid of natural numbers excluding zero

Published on 28 Mar 2026 - 8:09

score 81 · Answer 5 · 2017-07-29 11:24:44

81

Views

let $C(x)$ be the free vector space generated by $X$.Then if $Y$ is a second set, $C(X \cup Y) = C(X) \oplus C(Y)$

Published on 29 Jul 2017 - 11:24

score 435 · Answer 6 · 2026-03-28 01:47:23

435

Views

Group Presentations and Cayley graphs

Published on 28 Mar 2026 - 1:47

score 220 · Answer 7 · 2017-08-03 05:01:26

220

Views

Two rotations in $\mathbb R^3$ by irrational angle generate free group $F_2$.

Published on 03 Aug 2017 - 5:01

score 876 · Answer 8 · 2026-03-28 01:48:18

876

Views

Proof that dihedral group $D_{2n}$ is isomorphic to the group generated by two group elements of order 2

Published on 28 Mar 2026 - 1:48

score 4.8k · Answer 9 · 2017-08-06 14:36:34

4.8k

Views

The free group $Z*Z$ is isomorphic to which group?

Published on 06 Aug 2017 - 14:36

score 147 · Answer 10 · 2017-08-19 06:58:21

147

Views

Is a free group of finite rank $r>1$ polycyclic by finite?

Published on 19 Aug 2017 - 6:58

score 60 · Answer 11 · 2017-08-23 06:32:21

60

Views

I know that $G$ is finitely generated free group with generating set $S$, $G=\langle S\rangle $. Is $G$, free with base $S$?

Published on 23 Aug 2017 - 6:32

score 201 · Answer 12 · 2017-09-03 20:22:14

201

Views

Is the free group of uncountable rank a Lie group?

Published on 03 Sep 2017 - 20:22

score 261 · Answer 13 · 2017-09-03 21:49:08

261

Views

Q: Commutator subgroup of free group of infinite rank

Published on 03 Sep 2017 - 21:49

score 82 · Answer 14 · 2017-09-10 01:01:45

82

Views

Question about a homomorphism from free group to $\mathbb{Z}/2\mathbb{Z}$

Published on 10 Sep 2017 - 1:01

score 753 · Answer 15 · 2017-09-10 18:13:02

753

Views

Center of free group (of rank greater than 1) is trivial

Published on 10 Sep 2017 - 18:13

List Question

If $F$ is free with basis $X$ and if $F'$ is the commutator subgroup of $F$, then $F/F'$ is free abelian with basis all cosets $xF'$ with $x \in X$

What is a simple example of a free group?

Did the author switch notation in a proof and redefine things?

Free monoid of natural numbers excluding zero

let $C(x)$ be the free vector space generated by $X$.Then if $Y$ is a second set, $C(X \cup Y) = C(X) \oplus C(Y)$

Group Presentations and Cayley graphs

Two rotations in $\mathbb R^3$ by irrational angle generate free group $F_2$.

Proof that dihedral group $D_{2n}$ is isomorphic to the group generated by two group elements of order 2

The free group $Z*Z$ is isomorphic to which group?

Is a free group of finite rank $r>1$ polycyclic by finite?

I know that $G$ is finitely generated free group with generating set $S$, $G=\langle S\rangle $. Is $G$, free with base $S$?

Is the free group of uncountable rank a Lie group?

Q: Commutator subgroup of free group of infinite rank

Question about a homomorphism from free group to $\mathbb{Z}/2\mathbb{Z}$

Center of free group (of rank greater than 1) is trivial

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