Question

Prove that the groups $\langle a,b \mid ababa=babab \rangle$ and $\langle x,y \mid x^2=y^5 \rangle$ are isomorphic

score 340 · Answer 1 · 2026-03-25 06:12:55

340

Views

Prove that the groups $\langle a,b \mid ababa=babab \rangle$ and $\langle x,y \mid x^2=y^5 \rangle$ are isomorphic

Published on 25 Mar 2026 - 6:12

score 251 · Answer 2 · 2026-02-23 13:37:49

251

Views

Is this surjective homomorphism necessarily injective? (Free Product of Cyclic groups)

Published on 23 Feb 2026 - 13:37

score 37 · Answer 3 · 2018-07-06 15:32:35

37

Views

Problem understanding this statement (Kuhn's Annals paper on Subgroup Theorems of Groups)

Published on 06 Jul 2018 - 15:32

score 30 · Answer 4 · 2018-07-09 07:21:14

30

Views

the intersection of a basis of a free group with each subgroup in a continuous chain of subgroups

Published on 09 Jul 2018 - 7:21

score 96 · Answer 5 · 2018-07-11 15:39:57

96

Views

$\mathbb Z^2\subset G$ implies $F\not \stackrel{f.i.}{\subset} G$

Published on 11 Jul 2018 - 15:39

score 61 · Answer 6 · 2018-07-23 16:52:51

61

Views

Maximal Free Subgroup

Published on 23 Jul 2018 - 16:52

score 258 · Answer 7 · 2018-07-23 23:06:56

258

Views

Free group of a group

Published on 23 Jul 2018 - 23:06

score 65 · Answer 8 · 2018-07-25 14:32:36

65

Views

Free groups : Isomorphism beetween the free group $F_{X}$ and a group $F$

Published on 25 Jul 2018 - 14:32

score 454 · Answer 9 · 2026-03-25 07:45:09

454

Views

Can we show that every subgroup of a free group is free using Kurosh's theorem?

Published on 25 Mar 2026 - 7:45

score 118 · Answer 10 · 2018-07-31 01:38:00

118

Views

If $G$ is free on $A$ and on $B$, then $|A|=|B|$.

Published on 31 Jul 2018 - 1:38

score 142 · Answer 11 · 2018-07-31 17:32:26

142

Views

Property of free group from categorical definition

Published on 31 Jul 2018 - 17:32

score 480 · Answer 12 · 2018-08-08 14:55:37

480

Views

Are free groups simple?

Published on 08 Aug 2018 - 14:55

score 1.2k · Answer 13 · 2018-08-08 15:32:59

1.2k

Views

Prove that every subgroup of a free group is normal

Published on 08 Aug 2018 - 15:32

score 336 · Answer 14 · 2018-08-10 20:59:50

336

Views

Royal Road to Free Groups and Free Products

Published on 10 Aug 2018 - 20:59

score 130 · Answer 15 · 2018-08-16 16:15:06

130

Views

Confusion on the definition of presentation of Groups

Published on 16 Aug 2018 - 16:15

List Question

Prove that the groups $\langle a,b \mid ababa=babab \rangle$ and $\langle x,y \mid x^2=y^5 \rangle$ are isomorphic

Is this surjective homomorphism necessarily injective? (Free Product of Cyclic groups)

Problem understanding this statement (Kuhn's Annals paper on Subgroup Theorems of Groups)

the intersection of a basis of a free group with each subgroup in a continuous chain of subgroups

$\mathbb Z^2\subset G$ implies $F\not \stackrel{f.i.}{\subset} G$

Maximal Free Subgroup

Free group of a group

Free groups : Isomorphism beetween the free group $F_{X}$ and a group $F$

Can we show that every subgroup of a free group is free using Kurosh's theorem?

If $G$ is free on $A$ and on $B$, then $|A|=|B|$.

Property of free group from categorical definition

Are free groups simple?

Prove that every subgroup of a free group is normal

Royal Road to Free Groups and Free Products

Confusion on the definition of presentation of Groups

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