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
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!
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Gili Schul   <gili.schul@mail.huji.ac.il>