List questions from group-presentation

Published on 25 Mar 2026 - 18:56

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Presentation $\langle x,y \mid x^3=y^3=(xy)^3=1\rangle\cong\langle t\rangle\ltimes A$

Published on 25 Mar 2026 - 18:56

1.7k

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Fundamental groups of the Klein bottle and torus

Published on 25 Mar 2026 - 12:53

399

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Showing $\langle x,y\mid x^p=y^p=(xy)^p=1\rangle$ is infinite if $p>2, p$ prime.

Published on 25 Mar 2026 - 18:59

151

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Presentations: fewer relations than generators implies $G$ infinite.

Published on 25 Mar 2026 - 18:58

133

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Injective homomorphisms between group presentations

Published on 14 Jan 2020 - 13:50

441

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Suppose that $G$ is a group with $n$ generators and $r$ relations whether $r < n$. Prove that $G$ is infinite.

Published on 25 Mar 2026 - 18:57

65

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Presentations, automorphisms and natural homomorphisms.

Published on 25 Mar 2026 - 18:58

169

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Find a presentation with generators $g = (1,2)$ and $h = (2, 3)$ and three relations.

Published on 25 Mar 2026 - 20:18

35

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Presentation of the quaternion group

Published on 18 Jan 2020 - 7:36

71

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Show that $\langle s,t \mid t^2, tst^{-1}s \rangle \cong \langle a,b \mid a^2, b^2 \rangle$.

Published on 25 Mar 2026 - 20:19

103

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finitely presented group with finite generating set

Published on 10 Feb 2020 - 18:08

144

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Is $\langle a, b \mid baba^{-1}\rangle$ truly isomorphic to $\langle a, c \mid a^2c^2\rangle$?

Published on 25 Mar 2026 - 9:26

296

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Second derived subgroup of Baumslag Solitar group BS(2,3)

Published on 29 Feb 2020 - 14:59

93

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Is there an algorithm that, given a finite presentation of a free group, outputs a free basis for the group?

Published on 05 Mar 2020 - 3:00

List Question

A presentation of the infinite dihedral group.

Presentation $\langle x,y \mid x^3=y^3=(xy)^3=1\rangle\cong\langle t\rangle\ltimes A$

Fundamental groups of the Klein bottle and torus

Showing $\langle x,y\mid x^p=y^p=(xy)^p=1\rangle$ is infinite if $p>2, p$ prime.

Presentations: fewer relations than generators implies $G$ infinite.

Injective homomorphisms between group presentations

Suppose that $G$ is a group with $n$ generators and $r$ relations whether $r < n$. Prove that $G$ is infinite.

Presentations, automorphisms and natural homomorphisms.

Find a presentation with generators $g = (1,2)$ and $h = (2, 3)$ and three relations.

Presentation of the quaternion group

Show that $\langle s,t \mid t^2, tst^{-1}s \rangle \cong \langle a,b \mid a^2, b^2 \rangle$.

finitely presented group with finite generating set

Is $\langle a, b \mid baba^{-1}\rangle$ truly isomorphic to $\langle a, c \mid a^2c^2\rangle$?

Second derived subgroup of Baumslag Solitar group BS(2,3)

Is there an algorithm that, given a finite presentation of a free group, outputs a free basis for the group?

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