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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Bounds for the diameters of orbital graphs of affi
ne groups - Attila Maróti (Alfréd Rényi Institute
of Mathematics\,Hungarian Academy of Sciences)
DTSTART;TZID=Europe/London:20220621T111500
DTEND;TZID=Europe/London:20220621T121500
UID:TALK175622AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175622
DESCRIPTION:Let $G$ be a permutation group acting on a finite
set $X$. An orbital graph of $G$ is a graph with v
ertex set $X$ whose arc set is an orbit of $G$ on
$X \\times X$. An orbital graph whose arcs are a s
ubset of the diagonal $\\{ (x\,x) \\mid x \\in X \
\}$ is called a diagonal orbital graph. A famous t
heorem of Higman states that a transitive permutat
ion group $G$ acting on $X$ is primitive if and on
ly if all non-diagonal orbital graphs are (strongl
y) connected. A description of infinite families o
f finite primitive permutation groups for which th
ere is a uniform finite upper bound on the\n(undir
ected) diameter of all non-diagonal orbital graphs
has been given in a paper by Liebeck\, Macpherson
\, Tent. In this talk we will be interested in dia
meters of orbital graphs of affine primitive permu
tation groups. This is joint work with Saveliy V.
Skresanov
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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