Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 210

Preprint Number 210

Previous Next Preprint server

210. Martin W. Liebeck, Dugald Macpherson, Katrin Tent
Primitive permutation groups of bounded orbital diameter

Submission date: 24 October 2009.


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.

Mathematics Subject Classification: 20B15 (primary), 03C60 (secondary)

Keywords and phrases: primitive permutation group, pseudofinite field, supersimple theory

Full text: pdf, dvi, ps.

Last updated: October 30 2009 16:09 Please send your corrections to: