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 M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20250509T083153Z
DTSTART:20250513T130000Z
DTEND:20250513T140000Z
SUMMARY:HIMR-sponsored Algebra seminar - Colva Roney-Dougal
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}a1z4-m8q19x
 7m-pl8d42
DESCRIPTION:Title: Asymptotic enumeration of permutation groups\n\nAbstra
 ct: One of the most elementary\, but difficult\, questions we can ask ab
 out a finite group G is how many subgroups it has. An elementary argumen
 t shows that the symmetric group on n points has at least 2^{n^2/16} sub
 groups. Pyber showed in 1993 that it has at most 24^{n^2/6 + o(n^2)} sub
 groups\, and conjectured that the elementary lower bound is\, up to erro
 r terms\, the correct upper bound. This talk will present some ideas fro
 m our recent proof of this conjecture.\n\nOne reason for enumerating the
 se groups is to determine properties of randomly-chosen permutation grou
 ps. Erdos conjectured that if m \\leq 2^a then the number of groups of o
 rder m is bounded above by the number of groups of order 2^a\, and build
 ing on this Pyber conjectured in 1993 that as m tends to infinity the pr
 obability that a random group of order at most m is nilpotent tends to 1
 . In a similar vein\, Kantor conjectured in 1993 that the probability th
 at a random subgroup of the symmetric group on n points is nilpotent ten
 ds to 1. I will show that one of these conjectures is false.\n\nJoint wo
 rk with Gareth Tracey (Warwick).
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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