Computing in groups of Lie type with Lie algebras

                         Scott H Murray
                          Eindhoven


I will discuss recent progress in using Lie algebras to compute in
groups of Lie type.  In the case of finite fields, the Lie
correspondence between groups of Lie type and Lie algebras often fails.
This is why the classification of groups of Lie type avoids
the use of Lie algebras in favour of an approach via algebraic groups and
varieties.  However a lot of information about groups can still be derived
by studying their Lie algebras.  Since Lie algebras are linear, this
information can be found in a computationally efficient manner.
The two main application we will discuss are computing Sylow subgroups
and conjugacy problems.