List questions from group-presentation

Published on 09 Oct 2019 - 14:15

116

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About the order of element in $GL_2(\mathbb{Z})$

Published on 22 Mar 2026 - 6:09

255

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Commutator subgroup of a group of order $8q$, where $q$ is odd prime.

Published on 13 Oct 2019 - 12:39

137

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Commutator subgroup of $G=\langle a,b,c,d:a^4=b^2=c^2=d^q=1,ab=ba,ac=ca,bc=cb,d^{-1}ad=b,d^{-1}bd=c,d^{-1}cd=ab \rangle$

Published on 14 Oct 2019 - 12:45

50

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Map from group $G$ to $GL_n(\Bbb Q)$

Published on 14 Oct 2019 - 19:16

59

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Split exact sequence

Published on 23 Mar 2026 - 2:12

119

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Cardinality of a group with presentation

Published on 16 Oct 2019 - 17:28

47

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Presentation of $Q_{4n}$, $n \in \mathbb{N}$

Published on 18 Oct 2019 - 7:05

218

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Presentation of ${\rm SL}(2,3)$

Published on 20 Oct 2019 - 12:22

86

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Finding a normal form for the group given by $\langle a,t| t^{-1}at = a^{2}\rangle.$

Published on 25 Mar 2026 - 17:24

96

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Finding the order of a group using coset enumeration given the group presentation

Published on 07 Nov 2019 - 2:14

497

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Finding a presentation of a permutation group given the generators

Published on 08 Nov 2019 - 15:15

409

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Non-trivial semidirect product $\mathbb Z_3\rtimes Q_8$ is isomorphic to dicyclic group of order $24$

Published on 25 Mar 2026 - 17:21

65

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Assume $k|n$, show $D_{2n}/\langle r_n^k \rangle \cong D_{2k}$

Published on 13 Nov 2019 - 14:52

96

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What is a presentation of a group?

Published on 22 Nov 2019 - 6:34

List Question

Proving the order of quaternion group is 8

About the order of element in $GL_2(\mathbb{Z})$

Commutator subgroup of a group of order $8q$, where $q$ is odd prime.

Commutator subgroup of $G=\langle a,b,c,d:a^4=b^2=c^2=d^q=1,ab=ba,ac=ca,bc=cb,d^{-1}ad=b,d^{-1}bd=c,d^{-1}cd=ab \rangle$

Map from group $G$ to $GL_n(\Bbb Q)$

Split exact sequence

Cardinality of a group with presentation

Presentation of $Q_{4n}$, $n \in \mathbb{N}$

Presentation of ${\rm SL}(2,3)$

Finding a normal form for the group given by $\langle a,t| t^{-1}at = a^{2}\rangle.$

Finding the order of a group using coset enumeration given the group presentation

Finding a presentation of a permutation group given the generators

Non-trivial semidirect product $\mathbb Z_3\rtimes Q_8$ is isomorphic to dicyclic group of order $24$

Assume $k|n$, show $D_{2n}/\langle r_n^k \rangle \cong D_{2k}$

What is a presentation of a group?

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