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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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