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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:Base sizes of almost quasisimple groups and Pyber'
s conjecture - Melissa Lee\, Imperial College Lond
on
DTSTART;TZID=Europe/London:20180119T150000
DTEND;TZID=Europe/London:20180119T160000
UID:TALK85781AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/85781
DESCRIPTION:A _base_ of a permutation group $G$ acting on $\\O
mega$ is a subset of $\\Omega$ whose pointwise sta
biliser in $G$ is trivial. Bases have their origi
ns in computational group theory\, where they were
used to efficiently store permutation groups of l
arge degree into a small amount of computer memory
.\nThe minimal base size of $G$ is denoted by $b(G
)$.\nA well-known conjecture made by Pyber in 1993
states that there is an absolute constant $c$ suc
h 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 est
ablished in 2016 by Duyan\, Halasi and Maroti.\nIn
this talk\, I will cover some of the history and
uses of bases\, and discuss Pyber's conjecture\, e
specially in the context of primitive linear group
s\, and present some results on the determination
of the constant $c$ for bases of almost quasisimpl
e linear groups.
LOCATION:CMS\, MR14
CONTACT:Nicolas DuprÃ©
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