Maximal finite subgroups and minimal classes

Renaud Coulangeon (1) , Gabriele Nebe (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Lehrstuhl II für Mathematik

We apply Voronoi's algorithm to compute representatives of the conjugacy classes of maximal finite subgroups of the unit group of a maximal order in some simple $\QQ $-algebra. This may be used to show in small cases that non-conjugate orders have non-isomorphic unit groups.

Domaines: Théorie des nombres [math.NT]; Théorie des groupes [math.GR]

Renaud Coulangeon, Gabriele Nebe. Maximal finite subgroups and minimal classes. L'Enseignement Mathématique , 2014, 11 p. ⟨hal-00984173⟩