List questions from group-presentation

Published on 22 Mar 2026 - 5:22

58

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Could $\langle \Gamma | R \rangle \cong \langle \Gamma | S\rangle$ if $\langle R\rangle \subsetneq \langle S\rangle$?

Published on 22 Mar 2026 - 1:56

303

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What is an algorithm for determining if a finitely presented group is finite

Published on 22 Mar 2026 - 3:50

114

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Quaternion Group: Determine that $i^4 = 1$.

Published on 22 Mar 2026 - 9:10

230

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Can I conclude that my group is finitely generated, if it is a homomorphic image of a free-group on finitely many generators?

Published on 22 Mar 2026 - 9:32

133

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Proving the Free Abelian Group is Free Abelian...?

Published on 22 Mar 2026 - 2:32

295

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If we are handed the presentation $\langle i,j,k \mid i^2=j^2=k^2=ijk \rangle$ and nothing more, can we deduce that this is the quaternion group?

Published on 21 Mar 2026 - 20:20

245

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$p$-completion is pro-$p$ free

Published on 25 Mar 2026 - 1:15

717

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How to show that $|D_{2n}| = 2n$ via the presentation?

Published on 22 Mar 2026 - 10:06

35

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Symmetrising the relations in a presentation of a group

Published on 21 Mar 2026 - 17:35

46

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Is this proof that $\widehat{G_p}$ is pro-$p$ free correct?

Published on 25 Mar 2026 - 1:16

107

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Is there a way to describe the structure of $Aut(UT(3, p))$?

Published on 14 Mar 2019 - 6:08

85

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Is it generally true that $\langle a,b \rangle \cong \langle c,d \rangle\Rightarrow \text{ either }|a|=|c|,|b|=|d| \text{ or } |a|=|d|,|b|=|c|$?

Published on 15 Mar 2019 - 17:40

50

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Find the isomorphism type

Published on 18 Mar 2019 - 23:51

266

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Certain Isomorphic Representations of the dihedral group $D_{3}$

Published on 20 Mar 2019 - 2:01

List Question

How do I turn a group presentation into a multiplication table?

Could $\langle \Gamma | R \rangle \cong \langle \Gamma | S\rangle$ if $\langle R\rangle \subsetneq \langle S\rangle$?

What is an algorithm for determining if a finitely presented group is finite

Quaternion Group: Determine that $i^4 = 1$.

Can I conclude that my group is finitely generated, if it is a homomorphic image of a free-group on finitely many generators?

Proving the Free Abelian Group is Free Abelian...?

If we are handed the presentation $\langle i,j,k \mid i^2=j^2=k^2=ijk \rangle$ and nothing more, can we deduce that this is the quaternion group?

$p$-completion is pro-$p$ free

How to show that $|D_{2n}| = 2n$ via the presentation?

Symmetrising the relations in a presentation of a group

Is this proof that $\widehat{G_p}$ is pro-$p$ free correct?

Is there a way to describe the structure of $Aut(UT(3, p))$?

Is it generally true that $\langle a,b \rangle \cong \langle c,d \rangle\Rightarrow \text{ either }|a|=|c|,|b|=|d| \text{ or } |a|=|d|,|b|=|c|$?

Find the isomorphism type

Certain Isomorphic Representations of the dihedral group $D_{3}$

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