Generalised sifting in black-box groups

We generalise a sifting procedure introduced originally by Sims for computation
with permutation groups. Our version is given in the context of black-box 
groups, and is based on a chain of subsets rather than a subgroup chain. We 
apply our procedure to solve the constructive recognition problem for 
black-box sporadic simple groups and black-box general linear groups. Our 
algorithms are implemented in the GAP computational algebra system and 
experiments show that they work well in practice. Their theoretical complexity 
is also estimated. This is joint work with Sophie Ambrose, Scott Murray, 
Max Neunhöffer, and Cheryl Praeger.