List questions from group-presentation

Published on 10 May 2026 - 10:11

121

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Nilpotent Quotient Algorithm

Published on 10 May 2026 - 15:48

57

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What subgroup of $S_4$ is this?

Published on 14 Apr 2026 - 11:19

101

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To change deficiency of a group presentation

Published on 14 Apr 2026 - 12:06

364

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Perfect finite groups with balanced presentations

Published on 10 May 2026 - 19:45

101

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How to prove that this group has at most order 16

Published on 13 Apr 2026 - 11:29

89

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Extending group homomorpisms by defining image of generators.

Published on 09 Apr 2026 - 6:51

175

Views

Free nilpotent group on 2 generators of class 2.

Published on 11 Apr 2026 - 17:15

28

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

Published on 14 Apr 2026 - 1:09

128

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

Published on 16 Apr 2026 - 3:44

105

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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 17 Apr 2026 - 4:48

176

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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 26 Apr 2026 - 6:08

309

Views

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

Published on 10 May 2026 - 19:47

215

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Isomorphism between two finitley presented groups which are not finite

Published on 10 May 2026 - 18:01

138

Views

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 10 May 2026 - 19:47

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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