Chamber systems, geometries and parabolic systems whose diagram contains only bonds of strength 1 and 2
This paper contributes to the classification of locally finite transitive chamber systems of rank \(\geq 3\). It namely pins down the possibilities for such chamber systems in characteristic 2 assuming the diagram contains at least one bond of strength 2 (i.e. the star of at least one cell of cotype 2 is the chamber system of a generalized quadrangle), but none of strength \(>2\) and moreover, no star of type \(C_ 3\) or \(A_ 3\) (``polar'' or projective 3-space) has the alternating group Alt(7) as induced automorphism group. A similar result is known for geometries containing a star (or residue) related to Alt(7), so this finishes the characteristic 2 case with still the other restrictions above. (The case of characteristic \(>3\) is handled by \textit{F. G. Timmesfeld}, Invent. Math. 87, 603-641 (1987; Zbl 0607.20019)].)
scientific article; zbMATH DE number 4165882
scientific article