Deformation theory and finite simple quotients of triangle groups
Event details
| Date | 15.04.2013 |
| Hour | 09:00 › 10:15 |
| Speaker | Claude Marion [Fribourg] |
| Location |
MA A3 31
|
| Category | Conferences - Seminars |
Let 2≤a≤b≤c∈N with 1/a+1/b+1/c<1 and T be the triangle group 〈x,y,z : x^a = y^b = z^c = xyz = 1〉. Many papers have been dedicated to the question of which finite (simple) groups G(Fq) are quotients of T, or in other words when the equations above can be solved in G(Fq) with x, y and z generating G(Fq). Two main methods have been applied: explicit or probabilistic ones. We offer a third method: using deformation theory to study these equations in G(C). This new approach gives some systematic explanation of when groups of type G(Fq) are quotient of a given T. Along the way, we answer a question of Guralnick showing that every T is saturated with quotients of type E8(q). (Joint work with Larsen and Lubotzky.)
Practical information
- Expert
- Free
Organizer
- Jacques Thévenaz
Contact
- Jacques Thévenaz