Embeddings of PSL(2,41) and PSL(2,49) in E_8( C )

摘要

We classify embeddings of the finite simple groups PSL(2,41) and PSL (2,49) into algebraic groups of type E_8 in characteristic not dividing the orders of these respective groups. Lie theory and finite group theory point to families of elements in a group of type E_8 over a finite field which might satisfy a presentation for our finite simple group. Techniques from computational representation theory identify all suitable systems of generators. We describe a number of methods of computation in Chevalley groups of type E_8.