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Characterizations by Automorphism Groups of Some Rank 3 Buildings – IV: Hyperbolic p-adic Moufang Buildings of Rank 3

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Abstract

In this paper, we introduce the p-adic Moufang condition for hyperbolic buildings of rank 3. It is the most obvious and simplest generalization of the p-adic Moufang condition for affine buildings, introduced in Part III of this sequence of papers. We show that p is very restricted, which confirms (but does not prove) the conjecture that no p-adic analogue is possible for the construction of Moufang (hyperbolic) buildings by Ronan and Tits.

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References

  1. Gorenstein, D.: Finite Groups, Harper and Row, New York, 1968.

    Google Scholar 

  2. Ronan, M. A. and Tits J.: Building buildings, Math. Ann. 278 (1987), 291–306.

    Google Scholar 

  3. Tits J.: Classification of buildings of spherical type and Moufang polygons: a survey, Coll. Intern. Teorie Combin. Acc. Naz. Lincei, Roma 1973, Atti dei convegni Lincei 17 (1976), 229–246.

    Google Scholar 

  4. Tits J.: Quadrangles de Moufang, I, preprint (1976).

  5. Tits J.: Non-existence de certains polygones généralisés, I, Invent. Math. 36 (1976), 275–284.

    Google Scholar 

  6. Tits J.: Non-existence de certains polygones généralisés, II, Invent. Math. 51 (1979), 267–269.

    Google Scholar 

  7. Tits J.: Moufang octagons and the Ree groups of type 2 F 4, Amer. J. Math. 105 (1983), 539–594.

    Google Scholar 

  8. Van Maldeghem, H. and Van Steen, K.: Moufang affine buildings have Moufang spherical buildings at infinity, to appear in Glasgow Math. J.

  9. Van Maldeghem, H. and Van Steen K.: Characterizations by automorphism groups of some rank 3 buildings — I: Some properties of half strongly-transitive triangle buildings, Geom. Dedicata 73(2) (1998), 119–142.

    Google Scholar 

  10. Van Maldeghem, H. and Van Steen, K.: Characterizations by automorphism groups of some rank 3 buildings — II: A half strongly-transitive locally finite triangle building is a Bruhat-Tits building, Geom. Dedicata 74(2) (1999), 113–133.

    Google Scholar 

  11. Van Steen, K.: Characterizations by automorphism groups of some rank 3 buildings — III: Moufang-like conditions, Geom. Dedicata 74(3) (1999), 225–240.

    Google Scholar 

  12. Weiss, R.: The nonexistence of certain Moufang polygons, Invent. Math. 51 (1979), 261–266.

    Google Scholar 

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Authors and Affiliations

  1. Department of Pure Mathematics and Computer Algebra, University of Ghent, Galglaan 2, 9000, Gent, Belgium

    H. Van Maldeghem & K. Van Steen

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  1. H. Van Maldeghem
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  2. K. Van Steen
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Van Maldeghem, H., Van Steen, K. Characterizations by Automorphism Groups of Some Rank 3 Buildings – IV: Hyperbolic p-adic Moufang Buildings of Rank 3. Geometriae Dedicata 75, 115–122 (1999). https://doi.org/10.1023/A:1005001130872

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