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Primitive permutation groups of bounded orbital diameter
Author(s) -
Liebeck Martin W.,
Macpherson Dugald,
Tent Katrin
Publication year - 2010
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdp024
Subject(s) - mathematics , permutation (music) , combinatorics , bounded function , rank (graph theory) , upper and lower bounds , permutation group , permutation graph , finite field , simple (philosophy) , symmetric group , primitive permutation group , ultraproduct , cyclic permutation , discrete mathematics , mathematical analysis , graph , philosophy , physics , epistemology , acoustics
We give a description of infinite families of finite primitive permutation groups for which there is a uniform finite upper bound on the diameter of all orbital graphs. This is equivalent to describing families of finite permutation groups such that every ultraproduct of the family is primitive. A key result is that, in the almost simple case with socle of fixed Lie rank, apart from very specific cases, there is such a diameter bound. This is proved using recent results on the model theory of pseudofinite fields and difference fields.