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Hebrew University

Amitsur Algebra Seminar
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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>

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