Questions tagged [presentations-of-groups]

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12 votes
3 answers
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Database of finite presentations of used groups

Do You know any kind of database of presentations of groups? It may be on-line or off-line in form of tables, ideally case would be integrated in some Computer Algebra System. I am interested the ...
9 votes
3 answers
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Presentations of PSL(2, Z/p^n)

As is well known, the group $PSL(2,\mathbb Z)$ is isomorphic to the free product $C_2 \ast C_3$ of cyclic groups of order $2$ and $3$. Call the generators of the cyclic groups $S$ and $T$. Problem: ...
Łukasz Grabowski's user avatar
8 votes
3 answers
2k views

Are congruence subgroups of the modular group finitely presented?

Are the congruence subgroups of the modular group $\Gamma\equiv\mathrm{PSL}\left(2,\mathbb{Z}\right)$ (e.g. $\Gamma\left(n\right)$, $\Gamma_{0}\left(n\right)$, $\Gamma_{1}\left(n\right)$ etc.) ...
Jimeree's user avatar
  • 383
6 votes
1 answer
510 views

Relations in a particular subgroup of the braid group.

I think this should be a 10 minute exercise in a decent computer algebra package - unfortunately I'm hopelessly ignorant of such things, so I'm putting it up here in the hope that someone will be kind ...
Ed Segal's user avatar
  • 460