A diameter bound for extensions of the F4(2)-building

Authors:
A. A. Ivanov;A. Pasini
Affiliations:
Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ, UK;Department of Mathematics, University of Siena, via del Capitano 15, 53100 Siena, Italy
Venue:
European Journal of Combinatorics
Year:
2003

Citing 2
Cited 1

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Abstract

We consider extensions of the F4(2)-building with the diagram such that the residue of every element of the rightmost type is a one-point extension of the corresponding C3(2)-residue in the building. Four flag-transitive such geometries are known with the automorphism groups isomorphic to 2E6(2) : 2, 3 . 2E6(2) : 2, E6(2) : 2 and 226 : F4(2). The first example is a folding of the second one. We show that the last three examples are simply connected. This brings us close to the complete classification of the flag-transitive c-extensions of the F4(2)-building with the local one-point extension property.