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 341 · Answer 1 · 2026-05-10 14:07:31

341

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 10 May 2026 - 14:07

score 259 · Answer 2 · 2026-04-25 14:39:32

259

Views

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

Published on 25 Apr 2026 - 14:39

score 40 · Answer 3 · 2026-04-11 02:26:53

40

Views

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

Published on 11 Apr 2026 - 2:26

score 33 · Answer 4 · 2026-04-15 20:18:02

33

Views

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

Published on 15 Apr 2026 - 20:18

score 99 · Answer 5 · 2026-04-12 16:19:05

99

Views

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

Published on 12 Apr 2026 - 16:19

score 65 · Answer 6 · 2026-04-30 11:12:27

65

Views

Maximal Free Subgroup

Published on 30 Apr 2026 - 11:12

score 263 · Answer 7 · 2026-04-14 23:16:56

263

Views

Free group of a group

Published on 14 Apr 2026 - 23:16

score 67 · Answer 8 · 2026-04-14 21:53:27

67

Views

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

Published on 14 Apr 2026 - 21:53

score 456 · Answer 9 · 2026-04-28 06:57:58

456

Views

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

Published on 28 Apr 2026 - 6:57

score 121 · Answer 10 · 2026-04-16 19:32:59

121

Views

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

Published on 16 Apr 2026 - 19:32

score 145 · Answer 11 · 2026-04-10 09:34:12

145

Views

Property of free group from categorical definition

Published on 10 Apr 2026 - 9:34

score 485 · Answer 12 · 2026-04-30 09:54:54

485

Views

Are free groups simple?

Published on 30 Apr 2026 - 9:54

score 1.2k · Answer 13 · 2026-04-16 04:39:14

1.2k

Views

Prove that every subgroup of a free group is normal

Published on 16 Apr 2026 - 4:39

score 340 · Answer 14 · 2026-04-14 02:47:10

340

Views

Royal Road to Free Groups and Free Products

Published on 14 Apr 2026 - 2:47

score 133 · Answer 15 · 2026-04-11 23:38:11

133

Views

Confusion on the definition of presentation of Groups

Published on 11 Apr 2026 - 23:38

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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