List questions from group-presentation

Published on 22 Mar 2026 - 22:08

190

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How can I show that $D_{2n} \cong C_n \rtimes C_2 $

Published on 25 Mar 2026 - 9:26

73

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How to classify the sets $M$ by their structures?

Published on 03 Apr 2019 - 9:51

214

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Understand the free group universal property applied to $D_n$

Published on 04 Apr 2019 - 21:40

54

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What is a simply presented group?

Published on 06 Apr 2019 - 11:27

241

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Proving $G := \langle a, b, c \mid abc^{-1}a^{-1}, bcb \rangle$ is not isomorphic to $H := \langle a, b \rangle$

Published on 22 Mar 2026 - 3:40

104

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Why is $\langle a,b|bab^{-1} a^{-1},a a \rangle$ isomorphic to $\Bbb Z_2 \oplus \Bbb Z$?

Published on 07 Apr 2019 - 20:54

68

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$\pi_1(M)=\langle a,b|b^{-1} b^{-1},a \rangle \cong \Bbb Z?$

Published on 23 Mar 2026 - 12:42

45

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Number of words of length N that reduce to the identity in a specific Coxeter group

Published on 10 Apr 2019 - 14:18

80

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Focal subgroup is normal

Published on 10 Apr 2019 - 14:35

121

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Finding the order of $\langle a,b | a^{8}=b^{2}=1, ab=ba^{3}\rangle.$

Published on 23 Mar 2026 - 7:54

1.8k

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Presentations of subgroups of S6 as permutations

Published on 17 Apr 2019 - 15:12

235

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If we add more relations to a presentation will it always form a quotient group?

Published on 18 Apr 2019 - 2:26

359

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Is a HNN extension of a virtually torsion-free group virtually torsion-free?

Published on 23 Mar 2026 - 6:28

87

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Prove or disprove that $G = \langle{x,y\;|\; x^3, y^3, x^{13}, [x,y]=1}\rangle$ is trivial.

Published on 22 Mar 2026 - 18:17

List Question

Presentation of a group generated by reflections through hyperplane

How can I show that $D_{2n} \cong C_n \rtimes C_2 $

How to classify the sets $M$ by their structures?

Understand the free group universal property applied to $D_n$

What is a simply presented group?

Proving $G := \langle a, b, c \mid abc^{-1}a^{-1}, bcb \rangle$ is not isomorphic to $H := \langle a, b \rangle$

Why is $\langle a,b|bab^{-1} a^{-1},a a \rangle$ isomorphic to $\Bbb Z_2 \oplus \Bbb Z$?

$\pi_1(M)=\langle a,b|b^{-1} b^{-1},a \rangle \cong \Bbb Z?$

Number of words of length N that reduce to the identity in a specific Coxeter group

Focal subgroup is normal

Finding the order of $\langle a,b | a^{8}=b^{2}=1, ab=ba^{3}\rangle.$

Presentations of subgroups of S6 as permutations

If we add more relations to a presentation will it always form a quotient group?

Is a HNN extension of a virtually torsion-free group virtually torsion-free?

Prove or disprove that $G = \langle{x,y\;|\; x^3, y^3, x^{13}, [x,y]=1}\rangle$ is trivial.

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