Embeddings ofPSL(2, 41) andPSL(2, 49) inE8(C)

✍ Scribed by Robert L. Griess Jr.; A.J.E. Ryba

• Book ID: 102599882
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 363 KB
• Volume: 31
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.1999.1000

✦ Synopsis

We classify embeddings of the finite simple groups P SL(2, 41) and P SL(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 .