Question

Finitely Presented is Preserved by Extension

score 903 · Answer 1 · 2026-04-12 21:32:41

903

Views

Finitely Presented is Preserved by Extension

Published on 12 Apr 2026 - 21:32

score 428 · Answer 2 · 2026-04-13 22:54:36

428

Views

Showing that a group with a presentation is free/not free

Published on 13 Apr 2026 - 22:54

score 118 · Answer 3 · 2026-04-14 07:20:04

118

Views

Show that $\langle a,b | ababa \rangle $ is a presentation of $\mathbb{Z}$.

Published on 14 Apr 2026 - 7:20

score 797 · Answer 4 · 2026-04-14 20:47:38

797

Views

A finitely presented group $G$ is given by a presentation $\langle S,R\rangle$, where $R$ is finite. Show that $S$ is finite.

Published on 14 Apr 2026 - 20:47

score 2k · Answer 5 · 2026-04-15 21:59:00

2k

Views

Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?

Published on 15 Apr 2026 - 21:59

score 190 · Answer 6 · 2026-05-10 20:49:13

190

Views

Presentations that make the Todd-Coxeter algorithm blow up

Published on 10 May 2026 - 20:49

score 166 · Answer 7 · 2026-04-11 12:01:09

166

Views

Explicit description for $G=\langle a,b,c\mid[a,b]=b\,,\,[b,c]=c\,,\,[c,a]=a\rangle$

Published on 11 Apr 2026 - 12:01

score 801 · Answer 8 · 2026-04-12 08:17:52

801

Views

Cyclic Group Presentation

Published on 12 Apr 2026 - 8:17

score 138 · Answer 9 · 2026-04-17 14:03:24

138

Views

Group elements $x$ and $y$ satisfying $x^2 = y^2x^2y$ and $yx^{-1}y^2 = x^7$ commute.

Published on 17 Apr 2026 - 14:03

score 112 · Answer 10 · 2026-04-15 13:57:26

112

Views

Determine the center of this finitely presented group.

Published on 15 Apr 2026 - 13:57

score 102 · Answer 11 · 2026-04-12 08:40:33

102

Views

Another Presentation of Certain Cyclic Groups

Published on 12 Apr 2026 - 8:40

score 431 · Answer 12 · 2026-04-12 20:11:08

431

Views

Proving Finiteness of Group from Presentation

Published on 12 Apr 2026 - 20:11

score 131 · Answer 13 · 2026-04-10 00:59:31

131

Views

Presentations representing different groups.

Published on 10 Apr 2026 - 0:59

score 557 · Answer 14 · 2026-04-10 03:58:40

557

Views

Conditions for a finitely generated group with finite ordered generators

Published on 10 Apr 2026 - 3:58

score 118 · Answer 15 · 2026-04-14 11:07:34

118

Views

Finding a presentation of the quarternion group. (When do I know if I have given enough relations?)

Published on 14 Apr 2026 - 11:07

List Question

Finitely Presented is Preserved by Extension

Showing that a group with a presentation is free/not free

Show that $\langle a,b | ababa \rangle $ is a presentation of $\mathbb{Z}$.

A finitely presented group $G$ is given by a presentation $\langle S,R\rangle$, where $R$ is finite. Show that $S$ is finite.

Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?

Presentations that make the Todd-Coxeter algorithm blow up

Explicit description for $G=\langle a,b,c\mid[a,b]=b\,,\,[b,c]=c\,,\,[c,a]=a\rangle$

Cyclic Group Presentation

Group elements $x$ and $y$ satisfying $x^2 = y^2x^2y$ and $yx^{-1}y^2 = x^7$ commute.

Determine the center of this finitely presented group.

Another Presentation of Certain Cyclic Groups

Proving Finiteness of Group from Presentation

Presentations representing different groups.

Conditions for a finitely generated group with finite ordered generators

Finding a presentation of the quarternion group. (When do I know if I have given enough relations?)

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