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SUMMARY:Height and relational complexity for finite permutation groups - B
 ianca Loda\, University of South Wales
DTSTART:20180309T150000Z
DTEND:20180309T160000Z
UID:TALK98344@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:Height and relational complexity are two numerical invariants 
 that can be associated with any finite permutation group. The relational c
 omplexity of a finite permutation group was introduced by Cherlin in 1996.
  Very little is known about relational complexity in many specific cases a
 nd it can be rather difficult to compute it for any given permutation grou
 p.\n\nThe height of a finite permutation group on a set Ω  is defined as
  the maximum size of an independent set\, where a subset of Ω of is said
  to be independent if its pointwise stabilizer is not equal to the pointwi
 se stabilizer of a proper subset. It turns out that there exists a very us
 eful connection between the height and the relational complexity of a fini
 te permutation group. In particular\, the relational complexity is bounded
  in terms of the height of the group.\n\nIn this talk we will introduce th
 ese invariants and we will see how they are connected. Moreover\, we will 
 provide a computation of the height of all almost simple primitive groups 
 with socle PSL2(q) in their natural action on projective 1-space and this 
 will give us some information about the relational complexity of this acti
 on.\n
LOCATION:CMS\, MR14
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