This is a joint project by Oliver Braun, Renaud Coulangeon, Gabriele Nebe and Sebastian Schönnenbeck. The database contains generators and presentations of the S-unit groups of certain orders in various types of simple rational algebras of small degree. The project uses our other project Database of unit groups.

• Quaternion algebras over imaginary quadratic number fields
• Indefinite quaternion algebras over the rationals
• Rational division algebras of degree 3
• S-arithmetic subgroups of exceptional groups