Locally finite classical Tits chamber systems of large order

Timmesfeld, F. G.

doi:10.1007/bf01389245

Cited by 17 publications

(27 citation statements)

References 14 publications

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“…As any parabolic system in the sense of [16] yields a chamber system with the same diagram, we get a similar theorem for parabolic systems.…”

Section: Finite Classical Tits Geometries and Chamber Systems Of Charmentioning

confidence: 61%

“…Furthermore, from [16] we get that ifF is a classical Tits geometry over I with diagram A and flag-transitive automorphism group G, then C~(F) is a classical Tits chamber system over I with the same diagram A and G is a chamber transitive automorphism group of Cg(F). Then one can define the chamber system cg(F) in the following way: The chambers are the flags off of type I, two such chambers being/-adjacent if and only if they coincide in a flag of type I -{i).…”

Section: Finite Classical Tits Geometries and Chamber Systems Of Charmentioning

confidence: 98%

“…According to [11], [12], [15] and [16] we have yet to treat the case where the chamber system is defined over a field of characteristic 2 with a diagram containing bonds of strength > 2. For notations and definitions concerning chamber systems see [12] or [16]. Th.…”

Section: Finite Classical Tits Geometries and Chamber Systems Of Charmentioning

confidence: 99%

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A local classification of some finite classical tits geometries and chamber systems of characteristic ? 3

Stroth

1988

Geom Dedicata

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“…As any parabolic system in the sense of [16] yields a chamber system with the same diagram, we get a similar theorem for parabolic systems.…”

Section: Finite Classical Tits Geometries and Chamber Systems Of Charmentioning

confidence: 61%

Section: Finite Classical Tits Geometries and Chamber Systems Of Charmentioning

confidence: 98%

See 1 more Smart Citation

A local classification of some finite classical tits geometries and chamber systems of characteristic ? 3

Stroth

1988

Geom Dedicata

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“…In those cases, where the construction is possible, we end up with a Tits system (Go, B, N, R) of type A that has the property that B is finite while W = N/BnN is infinite, since the type A is nonspherical. This together is impossible by [Timl,(2.7)]. In the construction, we keep as close to Niles' notation as possible.…”

Section: Strong Parabolic Systems In Characteristicmentioning

confidence: 99%

Parabolic Systems: The GF(3) Case

Meixner¹

1993

Transactions of the American Mathematical Society

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Abstract.Parabolic systems defined over GF(q) have been classified by Timmesfeld for q > 4 and by Stroth for q = 2 (see references). We deal with the case q = 3 .Parabolic systems have been classified by Niles, Timmesfeld, Stroth, and Heiss, if the field of definition is G F (2) or has at least four elements. [Ni, Timl, Tim2, Tim5, Tim7, Stl, St2, St3, He]. We treat the GF(3) case, where only partial results by Thiel exist so far [Th]. Our result says that strong parabolic systems in characteristic 3 have spherical diagram, and therefore essentially generate only finite groups of Lie type with the same diagram. This is the content of Theorem A. If we drop the assumption that the parabolic systems have to be strong, some infinite families of systems occur, whose diagrams are or complete bipartite graphs with only double or triple bonds, and the systems are classified. This is Theorem B. The results of this paper are used in the determination of locally finite classical Tits chamber systems with a transitive group of automorphisms having finite chamber stabilizers. This classification, in turn, could be used in the proof of the theorem of Kantor, Liebler, and Tits that determines all classical affine buildings of rank at least 3 having a discrete chamber-transitive group of automorphisms.

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“…(iv) Assume that A is of rank at least 4, and that A is hyperbolic in the sense of[9], i.e. (iv) Assume that A is of rank at least 4, and that A is hyperbolic in the sense of[9], i.e.…”

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confidence: 99%