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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
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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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