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SUMMARY:Uncountably many maximal-closed subgroups of Sym(N) via reducts of
  Henson digraphs - Agarwal\, L (University of Leeds)
DTSTART:20151009T145000Z
DTEND:20151009T154500Z
UID:TALK61415@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:This work contributes to the two closely related areas of coun
 table homogeneous structures and infinite permutation groups. In the permu
 tation group side\, we answered a question of Macpherson that asked to sho
 w that there are uncountably many pairwise non-conjugate maximal-closed su
 bgroups of Sym(mathbb{N}). This was achieved by taking the automorphism gr
 oups of uncountably many pairwise non-isomorphic Henson digraphs. The fact
  these groups are maximal-closed follows from the classification of the re
 ducts of Henson digraphs. In itself\, this classification contributes to t
 he building list of structures whose reducts are known and also provides f
 urther evidence that Thomas' conjecture is true.\n\nIn this talk\, my main
  aim will be to describe the construction of these continuum many maximal-
 closed subgroups\, which will include Henson's famous construction of cont
 inuum many countable homogeneous digraphs. Any remaining time will be spen
 t giving some of the ideas behind how we prove these groups are maximal cl
 osed.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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