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SUMMARY:Base sizes of almost quasisimple groups and Pyber's conjecture - M
 elissa Lee\, Imperial College London
DTSTART:20180119T150000Z
DTEND:20180119T160000Z
UID:TALK85781@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:A _base_ of a permutation group $G$ acting on $\\Omega$ is a s
 ubset of $\\Omega$ whose pointwise stabiliser in $G$ is trivial.  Bases ha
 ve their origins in computational group theory\, where they were used to e
 fficiently store permutation groups of large degree into a small amount of
  computer memory.\nThe minimal base size of $G$ is denoted by $b(G)$.\nA w
 ell-known conjecture made by Pyber in 1993 states that there is an absolut
 e constant $c$ such that if $G$ acts primitively on $\\Omega$\, then $b(G)
  < c \\log |G| / \\log n$\, where $| \\Omega | = n$.\nAfter over 20 years 
 and contributions by a variety of authors\, Pyber's conjecture was establi
 shed in 2016 by Duyan\, Halasi and Maroti.\nIn this talk\, I will cover so
 me of the history and uses of bases\, and discuss Pyber's conjecture\, esp
 ecially in the context of primitive linear groups\, and present some resul
 ts on the determination of the constant $c$ for bases of almost quasisimpl
 e linear groups.
LOCATION:CMS\, MR14
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