List questions from group-presentation

Published on 12 Apr 2026 - 4:27

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Reidemeister-Schreier rewriting process. How to find the appropriate transversal element?

Published on 10 May 2026 - 19:47

392

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If I kill any element $g$ of a group $G$ and as a result $G/\langle\langle g\rangle\rangle$ is killed, is $G$ then cyclic?

Published on 10 May 2026 - 19:48

490

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A question about dihedral group

Published on 10 May 2026 - 19:45

249

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Presentation of Alternating group of order n

Published on 10 May 2026 - 19:48

144

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Using presentations, prove $\frac{\Bbb{Z} \times \Bbb{Z}}{\langle(3,3)\rangle}\cong\Bbb{Z} \times \Bbb{Z_3}$.

Published on 10 May 2026 - 20:53

99

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Is this a finitely generated subgroup of a finitely presented group?

Published on 10 May 2026 - 20:53

155

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Order of a group given group presentation.

Published on 11 Apr 2026 - 20:07

102

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Prove a group is equal to its commutator subgroup

Published on 10 May 2026 - 23:34

564

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Does my group generator have to be contained within the group it is generating

Published on 09 Apr 2026 - 13:29

247

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lamplighter group - presentation and relations

Published on 10 May 2026 - 22:04

144

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Given a set of generators of a group $G$, is there a method to find a presentation for $G$ using those generators?

Published on 10 May 2026 - 20:53

286

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Suppose $A=\langle a,b\mid ab^2a^{-1}b^{-3},ba^2b^{-1}a^{-3}\rangle.$ Show that $A \cong \{1\}$.

Published on 16 Apr 2026 - 13:03

154

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show trivial group

Published on 12 Apr 2026 - 15:22

1.4k

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Examples of non-finitely presented groups

Published on 10 May 2026 - 20:50

List Question

Present the group $\mathbb{Z}_{m} \times \mathbb{Z}_{n}$, where $\gcd(m, n) > 1$.

Reidemeister-Schreier rewriting process. How to find the appropriate transversal element?

If I kill any element $g$ of a group $G$ and as a result $G/\langle\langle g\rangle\rangle$ is killed, is $G$ then cyclic?

A question about dihedral group

Presentation of Alternating group of order n

Using presentations, prove $\frac{\Bbb{Z} \times \Bbb{Z}}{\langle(3,3)\rangle}\cong\Bbb{Z} \times \Bbb{Z_3}$.

Is this a finitely generated subgroup of a finitely presented group?

Order of a group given group presentation.

Prove a group is equal to its commutator subgroup

Does my group generator have to be contained within the group it is generating

lamplighter group - presentation and relations

Given a set of generators of a group $G$, is there a method to find a presentation for $G$ using those generators?

Suppose $A=\langle a,b\mid ab^2a^{-1}b^{-3},ba^2b^{-1}a^{-3}\rangle.$ Show that $A \cong \{1\}$.

show trivial group

Examples of non-finitely presented groups

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