List questions from group-presentation

Published on 05 Sep 2012 - 8:49

124

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Showing $H=\langle a,b|a^2=b^3=1,(ab)^n=(ab^{-1}ab)^k\rangle$.

Published on 27 Mar 2026 - 0:04

674

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Find the order of a group G from its presentation

Published on 27 Mar 2026 - 0:04

216

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Unusual presentation of a cyclic group.

Published on 01 Oct 2012 - 14:15

361

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Has every finite group a minimal presentation?

Published on 21 Oct 2012 - 3:44

107

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If $a^{3^3}=b^9=1$ for generators $a,b$ of $G$, can we conclude that $G$ is a $3$-group?

Published on 27 Mar 2026 - 15:19

135

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Finding a new presentation for $H=\langle ab,abc\rangle$

Published on 27 Mar 2026 - 0:09

3.7k

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Presentation of Rubik's Cube group

Published on 25 Mar 2026 - 23:10

166

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Peculiar presentation of Symmetric group of degree 10

Published on 16 Dec 2012 - 13:27

167

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Determining $\langle a,b,c\mid 6a+9b+6c=0, 8a+12b+4c=0\rangle^{\operatorname{ab}}.$

Published on 27 Mar 2026 - 2:01

880

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What are some slick ways to prove that a presentation is actually isomorphic to a given group?

Published on 16 Feb 2013 - 9:22

1.5k

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Generalized Quaternion Group

Published on 16 Feb 2013 - 11:29

2.1k

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Understanding presentations of groups

Published on 09 Mar 2013 - 19:08

414

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Does there exist a finite group with the following presentation?

Published on 10 Mar 2013 - 9:25

190

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Two questions about groups and presentations

Published on 20 Mar 2013 - 10:53

List Question

Is $\langle a,b \mid a^2b^2=1 \rangle$ a semidirect product of $\mathbb{Z}^2$ and $\mathbb{Z}_2$?

Showing $H=\langle a,b|a^2=b^3=1,(ab)^n=(ab^{-1}ab)^k\rangle$.

Find the order of a group G from its presentation

Unusual presentation of a cyclic group.

Has every finite group a minimal presentation?

If $a^{3^3}=b^9=1$ for generators $a,b$ of $G$, can we conclude that $G$ is a $3$-group?

Finding a new presentation for $H=\langle ab,abc\rangle$

Presentation of Rubik's Cube group

Peculiar presentation of Symmetric group of degree 10

Determining $\langle a,b,c\mid 6a+9b+6c=0, 8a+12b+4c=0\rangle^{\operatorname{ab}}.$

What are some slick ways to prove that a presentation is actually isomorphic to a given group?

Generalized Quaternion Group

Understanding presentations of groups

Does there exist a finite group with the following presentation?

Two questions about groups and presentations

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