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BEGIN:VEVENT
DTSTAMP:20210228T102946Z
DTSTART:20210416T100000Z
DTEND:20210416T110000Z
SUMMARY: Cheryl E Praeger - Coprime actions of finite groups - Pure Mathe
 matics Colloquium
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}q1l8-klp0hl
 hu-m247z0
DESCRIPTION:Speaker: Cheryl E Praeger\, University of Western Australia\n
 Series: Pure Mathematics Colloquium\n\n\nTitle: Coprime actions of finit
 e groups\nAbstract: Gabriel Navarro asked the following question:  Suppo
 se that\, for a finite linear group H acting completely reducibly on a f
 inite vector space V\, there are vectors a and b not fixed by H such tha
 t the H-orbits containing a and b have coprime lengths m and n. Is there
  an H-orbit on vectors of length mn?  We answered\, by showing that the 
 H-orbit containing a + b has length mn\, and by showing\, moreover\, tha
 t in this situation H cannot be irreducible on V.\n\nViewed differently 
 this tells us that a point-stabiliser in a finite affine primitive permu
 tation group cannot have a pair of orbits of coprime lengths. On the oth
 er hand\, stabilisers in different kinds of finite primitive permutation
  groups can have coprime orbits. Considering such groups led us to resol
 ving a question of Peter Neumann from 1973\, arising from a theorem of M
 arie Weiss n 1935. This is joint work with Silvio Dolfi\, Bob Guralnick 
 and Pablo Spiga.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
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