List questions from group-presentation

Published on 17 Nov 2017 - 19:02

120

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Identifying $\langle r,s\mid srs^{-2}r, r^{-1}srsr^{-1}\rangle$.

Published on 18 Nov 2017 - 14:37

146

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Identifying $\langle \{x_h\mid h\in H\}\mid \{x_{h'}x_{h'a}x_{h'b}^{-1}\mid h'\in H\}\rangle$ if $H=\langle a,b\mid a^2, b^4, ab=ba\rangle$.

Published on 19 Nov 2017 - 16:29

193

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Representation of elements by words on finite groups.

Published on 24 Nov 2017 - 17:51

85

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Conditions, under which a mapping of generators of a group induces an automorphism.

Published on 25 Nov 2017 - 20:20

99

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Presentations of groups

Published on 26 Mar 2026 - 22:12

430

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Finding the invariant factors of $G/G'$.

Published on 27 Mar 2026 - 0:06

332

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What is needed to specify a group?

Published on 13 Dec 2017 - 15:37

217

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Quotient of group given by presentation is finite

Published on 15 Dec 2017 - 0:32

386

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Understanding the Todd-Coxeter Coset Enumeration Algorithm.

Published on 26 Mar 2026 - 23:59

109

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Show that a group is trivial

Published on 20 Dec 2017 - 5:22

89

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Order of group $\langle x,y,z \mid x^2=y^2= z^2= e, xyz=yzx = zxy \rangle$

Published on 22 Dec 2017 - 7:27

227

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Presentation of $D_4$

Published on 27 Mar 2026 - 16:56

191

Views

Finding presentation of a subgroup in GAP

Published on 27 Mar 2026 - 0:10

115

Views

Is this group representation faithful? Von Dyck group (2,3,8).

Published on 02 Jan 2018 - 22:37

List Question

Given a presentation of a group, how do you find what it is isomorphic to?

Identifying $\langle r,s\mid srs^{-2}r, r^{-1}srsr^{-1}\rangle$.

Identifying $\langle \{x_h\mid h\in H\}\mid \{x_{h'}x_{h'a}x_{h'b}^{-1}\mid h'\in H\}\rangle$ if $H=\langle a,b\mid a^2, b^4, ab=ba\rangle$.

Representation of elements by words on finite groups.

Conditions, under which a mapping of generators of a group induces an automorphism.

Presentations of groups

Finding the invariant factors of $G/G'$.

What is needed to specify a group?

Quotient of group given by presentation is finite

Understanding the Todd-Coxeter Coset Enumeration Algorithm.

Show that a group is trivial

Order of group $\langle x,y,z \mid x^2=y^2= z^2= e, xyz=yzx = zxy \rangle$

Presentation of $D_4$

Finding presentation of a subgroup in GAP

Is this group representation faithful? Von Dyck group (2,3,8).

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