Hebrew University Amitsur Algebra Seminar --------------------------------------- Time: Thursday, Dec 8, 12:00 ~V 13:15 Place: math 209 Speaker: Claude Marion Title: Triangle generation of finite groups of Lie type and rigidity Abstract: This talk is about the $(p_1,p_2,p_3)$-generation problem for finite groups of Lie type, where we say that a finite group is $(p_1,p_2,p_3)$-generated if it is generated by two elements of orders $p_1$, $p_2$ whose product has order $p_3$. Given a triple $(p_1,p_2,p_3)$ of primes, we say that $(p_1,p_2,p_3)$ is rigid for a simple algebraic group $G$ if the sum of the dimensions of the subvarieties of elements of orders dividing $p_1$, $p_2$, $p_3$ in $G$ is equal to $2 \dim G$. We conjecture that if $(p_1,p_2,p_3)$ is a rigid triple for $G$ then given a prime $p$, there are only finitely many positive integers $r$ such that the finite group $G(p^r)$ is a $(p_1,p_2,p_3)$-group. We discuss this conjecture, classify the rigid triples of primes for simple algebraic groups and present a result stating that the conjecture holds in many cases. The conjecture together with this classification puts into context many results on Hurwitz $(2,3,7)$-generation in the literature, and motivates a new study of the $(p_1,p_2,p_3)$-generation problem for certain finite groups of Lie type of low rank. You are cordially invited! <http://math.huji.ac.il/amitsur.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Gili Schul <gili.schul@mail.huji.ac.il>