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UID:20250717T230632EDT-6623tSvP31@132.216.98.100
DTSTAMP:20250718T030632Z
DESCRIPTION:On finite simple images of triangle groups\n\nGiven a triple (a
 \, b\, c) of positive integers\, a finite group is said to be an (a\, b\, 
 c)-group if it is a quotient of the triangle group Ta\,b\,c = hx\, y\, z :
  x a = y b = z c = xyz = 1i. Let G0 = G(p r ) be a finite quasisimple grou
 p of Lie type with corresponding simple algebraic group G. Given a positiv
 e integer a\, let G[a] = {g ∈ G : g a = 1} be the subvariety of G consisti
 ng of elements of order dividing a\, and set ja(G) = dim G[a] . Given a tr
 iple (a\, b\, c) of positive integers\, we conjectured a few years ago tha
 t if ja(G) +jb(G) +jc(G) = 2 dim G then given a prime p there are only fin
 itely many positive integers r such that G(p r ) is an (a\, b\, c)-group. 
 We present some recent progress on this conjecture and related results: in
  particular the conjecture holds for finite simple groups.\n
DTSTART:20170510T144500Z
DTEND:20170510T144500Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Claude Marion\, University of Padova
URL:/mathstat/channels/event/claude-marion-university-
 padova-268019
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