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CATEGORIES:Junior Algebra/Logic/Number Theory seminar
SUMMARY:Height and relational complexity for finite permut
ation groups - Bianca Loda\, University of South W
ales
DTSTART;TZID=Europe/London:20180309T150000
DTEND;TZID=Europe/London:20180309T160000
UID:TALK98344AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/98344
DESCRIPTION:Height and relational complexity are two numerical
invariants that can be associated with any finite
permutation group. The relational complexity of a
finite permutation group was introduced by Cherli
n in 1996. Very little is known about relational c
omplexity in many specific cases and it can be rat
her difficult to compute it for any given permutat
ion group.\n\nThe height of a finite permutation g
roup on a set Ω is defined as the maximum size of
an independent set\, where a subset of Ω of is sa
id to be independent if its pointwise stabilizer i
s not equal to the pointwise stabilizer of a prope
r subset. It turns out that there exists a very us
eful connection between the height and the relatio
nal complexity of a finite permutation group. In p
articular\, the relational complexity is bounded i
n terms of the height of the group.\n\nIn this tal
k we will introduce these invariants and we will s
ee how they are connected. Moreover\, we will prov
ide a computation of the height of all almost simp
le primitive groups with socle PSL2(q) in their na
tural action on projective 1-space and this will g
ive us some information about the relational compl
exity of this action.\n
LOCATION:CMS\, MR14
CONTACT:Nicolas Dupré
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