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Chamber systems, geometries and parabolic systems whose diagram contains only bonds of strength 1 and 2. (English) Zbl 0709.51015
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 F. G. Timmesfeld, Invent. Math. 87, 603-641 (1987; Zbl 0607.20019)].)
Reviewer: H.Van Maldeghem

MSC:
51E24 Buildings and the geometry of diagrams
51B25 Lie geometries in nonlinear incidence geometry
20E42 Groups with a \(BN\)-pair; buildings
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References:
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