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SUMMARY:Ulla Karhumäki (University of Helsinki)
DTSTART:20250220T190000Z
DTEND:20250220T200000Z
DTSTAMP:20260423T052832Z
UID:OLS/167
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/167/">Ps
 eudofinite primitive permutation groups of finite SU-rank</a>\nby Ulla Kar
 humäki (University of Helsinki) as part of Online logic seminar\n\n\nAbst
 ract\nA (definably) primitive permutation group (G\,X) is a group G togeth
 er with a transitive faithful and definable action on X such that there ar
 e no proper nontrivial (definable) G-invariant equivalence relations on X.
  Definably primitive permutation groups of finite Morley rank are well-stu
 died: in particular\, it is shown by Macpherson and Pillay that such a gro
 up with infinite point stabilisers is actually primitive and by Borovik an
 d Cherlin that\, given such a group (G\,X)\, the Morley rank of G can be b
 ounded in terms of the Morley rank of X. We show similar results for a pse
 udofinite definably primitive permutation group (G\,X) of finite SU-rank: 
 we first show that (G\,X) is primitive if and only if the point stabiliser
 s are infinite. This then allows us to apply a classification result by Li
 ebeck\, Macpherson and Tent on (G\,X) so that we may bound the SU-rank of 
 G in terms of the SU-rank of X. This is joint work in with Nick Ramsey.\n
LOCATION:https://researchseminars.org/talk/OLS/167/
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