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(Almost strongly minimal) generalized n-gons are constructed for all n 3 for which the automorphism group acts transitively on the set of ordered ordinary (nj1)-gons contained in it, a new class of BN-pairs thus being obtained. Through the construction being modified slightly, 2 A ! many non-isomorphic almost strongly minimal generalized n-gons are obtained(More)
We show that any pseudofinite group with NIP theory and with a finite upper bound on the length of chains of centralisers is soluble-by-finite. In particular, any NIP rosy pseudofinite group is soluble-by-finite. This generalises, and shortens the proof of, an earlier result for stable pseudofinite groups. An example is given of an NIP pseudofinite group(More)
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(More)