Abstract
In Part 1 of this paper (see [7]), we studied the general theory of epimorphisms of generalized polygons, with emphasis on epimorphisms that do not preserve the diameter. Let us briefly recall the situation and relevant definitions.
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References
A. Blokhuis, personal communication.
R. Bödi and L. Kramer, On homomorphisms between generalized polygons, Geom. Dedicata 58 (1995), 1–14.
A.E. Brouwer, A non-degenerate generalized quadrangle with lines of size four is finite, Advances in Finite Geometries and Designs, Proceedings of the Third Isle of Thorns Conference (eds. J.W.P. Hirschfeld et al.), Oxford University Press, Oxford, 1991, 47–49.
P.J. Cameron, Orbits of permutation groups on unordered sets, II., J. London Math. Soc. 23 (1981), 49–264.
G. Cherlin, Notes on locally finite generalized quadrangles, 1996.
W. Feit and G. Higman, The nonexistence of certain generalized polygons, J. Algebra 1 (1964), 114–131.
R. Gramlich and H. Van Maldeghem, Epimorphisms of generalized polygons, Part 1: geometrical characterizations, Des. Codes Cryptogr. 21 (2000), 99–111.
W.H. Haemers and C. Roos, An inequality for generalized hexagons, Geom. Dedicata 10 (1981), 219–222.
D.G. Higman, Invariant relations, coherent configurations and generalized polygons, Combinatorics (eds. M. Hall and J.H. Van Lint), Proceedings ofthe Advanced Study Institute, Breukelen, 1974, Part 3: Combinatorial Group Theory, Reidel, Dordrecht, 1975, 347–363.
S.E. Payne and J.A. Thas, Finite Generalized Quadrangles, Pitman, London, 1984.
J. Tits, Sur la trialité et certains groupes qui s’en déduisent, Inst. Hautes Études Sci. Publ. Math. 2 (1959), 13–60.
J. Tits, Endliche Spiegelungsgruppen, die als Weylgruppen auftreten, Invent. Math. 43 (1977), 283–295.
H. Van Maldeghem, Generalized Polygons, Birkhäuser, Basel 1998.
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Gramlich, R., Van Maldeghem, H. (2001). Epimorphisms of Generalized Polygons, Part 2: Some Existence and Non-Existence Results. In: Blokhuis, A., Hirschfeld, J.W.P., Jungnickel, D., Thas, J.A. (eds) Finite Geometries. Developments in Mathematics, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0283-4_12
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DOI: https://doi.org/10.1007/978-1-4613-0283-4_12
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