Computing component groups of stabilizers of nilpotent orbit representatives

We describe computational methods for computing the component group of the stabilizer of a nilpotent element in a complex simple Lie algebra. Our algorithms have been implemented in the language of the computer algebra system GAP4. Occasionally we need Gr & ouml;bner basis computations; for these we use the systems MAGMA and SINGULAR. The resulting component groups have been made available in the GAP4 package SLA.