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SUMMARY:Orbit-coherence in permutation groups - John Britnell\, Imperial C
 ollege
DTSTART:20140604T153000Z
DTEND:20140604T163000Z
UID:TALK52923@talks.cam.ac.uk
CONTACT:David Stewart
DESCRIPTION:For a permutation g of a set X\, let p(g) be the partition of 
 X given by\nthe orbits of g. For a permutation group G on X\, let p(G) be 
 the set of\npartitions p(g) for g in G. The set of all partitions of X for
 ms a\ncomplete lattice under the refinement order\, and it makes sense to 
 look\nat the order-theoretic properties of the subset p(G).\n\nI shall tal
 k about joint work with Mark Wildon (Royal Holloway)\, on\npermutation gro
 ups G for which p(G) is an upper- or\nlower-semilattice. In either case\, 
 this is a highly restrictive\ncondition on G\, but there are many interest
 ing examples\, in both finite\nand infinite degree. In particular\, the ce
 ntralizer in Sym(X) of an\nelement g is always a lower-semilattice\, and\,
  subject to a\nfiniteness condition on the cycles of g\, a lattice.
LOCATION:MR12
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