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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Uncountably many maximal-closed subgroups of Sym(N
) via reducts of Henson digraphs - Agarwal\, L (Un
iversity of Leeds)
DTSTART;TZID=Europe/London:20151009T155000
DTEND;TZID=Europe/London:20151009T164500
UID:TALK61415AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61415
DESCRIPTION:This work contributes to the two closely related a
reas of countable homogeneous structures and infin
ite permutation groups. In the permutation group s
ide\, we answered a question of Macpherson that as
ked to show that there are uncountably many pairwi
se non-conjugate maximal-closed subgroups of Sym(m
athbb{N}). This was achieved by taking the automor
phism groups of uncountably many pairwise non-isom
orphic Henson digraphs. The fact these groups are
maximal-closed follows from the classification of
the reducts of Henson digraphs. In itself\, this c
lassification contributes to the building list of
structures whose reducts are known and also provid
es further evidence that Thomas' conjecture is tru
e.\n\nIn this talk\, my main aim will be to descri
be the construction of these continuum many maxima
l-closed subgroups\, which will include Henson's f
amous construction of continuum many countable hom
ogeneous digraphs. Any remaining time will be spen
t giving some of the ideas behind how we prove the
se groups are maximal closed.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:
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