Abstract
In this paper we give a method for constructing sharply 1-transitive permutation sets inside a finite permutation group with certain properties and we apply this method to obtain a family of sharply 1-transitive permutation subsets of the sharply 3-transitive permutation group M(p 2f) on PG(1, p 2f) for p f ≡ 1 (mod 4).
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References
Barlotti, A. and Strambach, K., ‘k-Transitive Permutation Groups and k-Planes’, Math. Z. 185 (1984), 465–485.
Benz, W., Vorlesungen über Geometrie der Algebren, Springer-Verlag, Berlin, Heidelberg, New York, 1973.
Bonisoli, A., ‘The Regular Subgroups of the Sharply 3-Transitive Finite Permutation Groups’ (submitted).
Fiori, C. and Zironi, F., ‘Esistenza e construzione di sottoinsiemi di permutazioni strettamente 1-transitivi’ (to appear in Atti Sem. Mat. Fis. Univ. Modena).
Fisher, J. C. and Thas, J. A., ‘Flocks in PG(3,q)’, Math. Z. 169 (1979), 1–11.
Huppert, B., Endliche Gruppen, I. Springer-Verlag, Berlin, Heidelberg, New York, 1967.
Huppert, B. and Blackburn, N., Finite Groups, III, Springer-Verlag, Berlin, Heidelberg, New York, 1982.
Segre B., Istituzioni di Geometria Superiore, Vol. III, Istituto Matematico ‘G. Castelnuovo’, Roma, 1965.
Wielandt H., Finite Permutation Groups, Academic Press, New York, 1964.
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Work supported by G.N.S.A.G.A. and M.P.I.
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Bonisoli, A., Fiori, C. Sharply 1-transitive subsets of certain permutation groups. Geom Dedicata 26, 309–314 (1988). https://doi.org/10.1007/BF00183022
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DOI: https://doi.org/10.1007/BF00183022