List questions from group-presentation

Published on 08 Jun 2019 - 16:44

119

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Nilpotent Quotient Algorithm

Published on 25 Mar 2026 - 1:24

54

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What subgroup of $S_4$ is this?

Published on 20 Jun 2019 - 15:13

98

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To change deficiency of a group presentation

Published on 21 Jun 2019 - 15:28

362

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Perfect finite groups with balanced presentations

Published on 21 Mar 2026 - 11:10

98

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How to prove that this group has at most order 16

Published on 29 Jun 2019 - 13:35

86

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Extending group homomorpisms by defining image of generators.

Published on 08 Jul 2019 - 21:02

174

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Free nilpotent group on 2 generators of class 2.

Published on 21 Mar 2026 - 18:20

25

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Elaboration of Tietze Equivalences $I, II, I', II'$.

Published on 26 Jul 2019 - 18:13

125

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Challenge: find the order of an element in a Finite Abelian Group with a given presentation

Published on 31 Jul 2019 - 13:59

102

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$G_1$ a subquotient of $G_2$ and $G_2$ a subquotient of $G_1$, is $G_1 \cong G_2$?

Published on 01 Aug 2019 - 15:38

170

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Showing $\langle a,p,q\mid p^{-1}ap=a^2, q^{-1}aq=a^2\rangle$ is non-hopfian (from first principles).

Published on 23 Feb 2026 - 13:39

307

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Showing $\left<a,b,c : a^2=b^3=c^5=abc \right>/\left<abc\right>$ is finite

Published on 20 Mar 2026 - 16:42

214

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Isomorphism between two finitley presented groups which are not finite

Published on 25 Mar 2026 - 11:10

136

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Showing $b^2 \notin \langle a \rangle$ for $V_{8n}=\langle a,b:a^{2n}=e, b^4 = e, ba=a^{-1}b^{-1},b^{-1}a=a^{-1}b\rangle.$

Published on 20 Mar 2026 - 17:47

List Question

Universal Property for Presentations

Nilpotent Quotient Algorithm

What subgroup of $S_4$ is this?

To change deficiency of a group presentation

Perfect finite groups with balanced presentations

How to prove that this group has at most order 16

Extending group homomorpisms by defining image of generators.

Free nilpotent group on 2 generators of class 2.

Elaboration of Tietze Equivalences $I, II, I', II'$.

Challenge: find the order of an element in a Finite Abelian Group with a given presentation

$G_1$ a subquotient of $G_2$ and $G_2$ a subquotient of $G_1$, is $G_1 \cong G_2$?

Showing $\langle a,p,q\mid p^{-1}ap=a^2, q^{-1}aq=a^2\rangle$ is non-hopfian (from first principles).

Showing $\left<a,b,c : a^2=b^3=c^5=abc \right>/\left<abc\right>$ is finite

Isomorphism between two finitley presented groups which are not finite

Showing $b^2 \notin \langle a \rangle$ for $V_{8n}=\langle a,b:a^{2n}=e, b^4 = e, ba=a^{-1}b^{-1},b^{-1}a=a^{-1}b\rangle.$

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