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Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.

4 votes
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What is the most efficient way to factor a matrix into a given set of generators?

As to your general question, there is a method which is better than the inefficient solution you give. -- Namely, compute spheres of radii $r = 1, 2, \dots$ with respect to the word metric about the i …
Stefan Kohl's user avatar
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8 votes
Accepted

Counting conjugacy classes in simple groups of Lie type

According to Fleischmann, Peter; Janiszczak, Ingo. On the computation of conjugacy classes of Chevalley groups. Appl. Alg. in Eng., Comm. and Comp. 1996, 7(3), 221--234 the class number of $ …
Stefan Kohl's user avatar
  • 19.6k
22 votes

Small-index subgroups of SL(3,Z)

In order to answer the question we need a finite presentation of ${\rm SL}(3,\mathbb{Z})$ and a general method to find all subgroups of index $\leq n$ of a finitely presented group: A finite present …
Stefan Kohl's user avatar
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