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 M3//EN
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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20241122T094423Z
DTSTART:20241126T140000Z
DTEND:20241126T150000Z
SUMMARY:Algebra seminar - Scott Harper
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}b14h-m34mg3
 0b-o7wvpl
DESCRIPTION:Title: Coverings of finite groups and derangements\nAbstract:
  A finite group is never the union of conjugates of a proper subgroup. E
 quivalently\, a nontrivial finite transitive permutation group always co
 ntains a derangement (a fixed-point-free permutation). This is a theorem
  of Jordan (1872) and it follows from a simple counting argument. I will
  discuss several variations on this theorem that have attracted attentio
 n over the decades\, highlighting connections with number theory\, graph
  theory and extremal combinatorics. I will then focus on the conjecture 
 that a finite group is never the union of conjugates of two proper subgr
 oups of the same size and discuss joint work with David Ellis towards th
 is. Along the way\, I will discuss recent work with Martin Liebeck on re
 presentations of extensions of simple groups\, generalising work of Feit
  and Tits (1978).
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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