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SUMMARY:Bounds for the diameters of orbital graphs of affine groups - Atti
 la Maróti (Alfréd Rényi Institute of Mathematics\,Hungarian Academy of 
 Sciences)
DTSTART:20220621T101500Z
DTEND:20220621T111500Z
UID:TALK175622@talks.cam.ac.uk
DESCRIPTION:Let $G$ be a permutation group acting on a finite set $X$. An 
 orbital graph of $G$ is a graph with vertex set $X$ whose arc set is an or
 bit of $G$ on $X \\times X$. An orbital graph whose arcs are a subset of t
 he diagonal $\\{ (x\,x) \\mid x \\in X \\}$ is called a diagonal orbital g
 raph. A famous theorem of Higman states that a transitive permutation grou
 p $G$ acting on $X$ is primitive if and only if all non-diagonal orbital g
 raphs are (strongly) connected. A description of infinite families of fini
 te primitive permutation groups for which there is a uniform finite upper 
 bound on the\n(undirected) diameter of all non-diagonal orbital graphs has
  been given in a paper by Liebeck\, Macpherson\, Tent. In this talk we wil
 l be interested in diameters of orbital graphs of affine primitive permuta
 tion groups. This is joint work with Saveliy V. Skresanov
LOCATION:Seminar Room 2\, Newton Institute
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