Advertisement

Annali di Matematica Pura ed Applicata (1923 -)

, Volume 116, Issue 1, pp 189–205 | Cite as

Una proprietà gruppale delle involuzioni planari che mutano in sé un'ovale di un piano proiettivo finito

  • Gabriele Korchmáros
Article

Summary

The purpose of the present paper is to prove the following theorem: Let Ω be an oval in the projective plane P of odd order n. If P admits a collineation group G wich maps Ω onto itself and is doubly transitive on Ω, then P is desarguesian, Ω is a conic and G contains all collineations in the little projective group PSL(2, n) of P wich leaves Ω invariant.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliografia

  1. [1]
    M. Aschbacher,On doubly transitive permutation groups of degree n = 2 (mod 4), Illinois J. Math.,16 (1969), pp. 276–279.MathSciNetzbMATHGoogle Scholar
  2. [2]
    H. Bender,Endliche zweifach transitive Permutationsgruppen deren Involutionen keine Fixpunte haben, Math. Zeitschr.,104 (1968), pp. 175–204.CrossRefGoogle Scholar
  3. [3]
    P. Dembowski,Finite Geometries, Springer Verlag (1968).Google Scholar
  4. [4]
    J. Cofman,Doubly transitivity in finite affine and projective planes, Proc. Proj. Geom. Conf., Univ. Illinois (1967), pp. 16–19.Google Scholar
  5. [5]
    Ch. Hering -W. M. Kantor -G. M. Seitz,Finite groups with a Split BN-pairs of Rank 1, J. Algebra,20 (1970), pp. 435–475.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Ch. Hering,Zweifach transitive Permutationsgruppen in denen zwei die maximale Anzahl von Fixpunten sind, Math. Zeitschr.,104 (1968), pp. 150–174.CrossRefGoogle Scholar
  7. [7]
    Ch. Hering,On 2-groups operating on projective planes, Illinois J. Math.,16 (1972), pp. 581–595.MathSciNetzbMATHGoogle Scholar
  8. [8]
    B. Huppert,Endliche Gruppen I, Springer Verlag (1967).Google Scholar
  9. [9]
    F. Kárteszi,Introduction to the finite geometries, Akadémiai Kiado (Budapest) (1975).Google Scholar
  10. [10]
    H. Lüneburg, Charakteriseirungen der endlichen desargueschen projektive Ebenen, Math. Zeitschr.,85 (1964), pp.419–450.CrossRefGoogle Scholar
  11. [11]
    D. S. Passman,Some 5/2-transitive permutation groups, Pacific J. Math.,13 (1969), pp. 755–1029.MathSciNetzbMATHGoogle Scholar
  12. [12]
    B. Segre,Lectures on Modern Geometry, Edizioni Cremonese (1961).Google Scholar
  13. [13]
    G. Zappa,Fondamenti di teoria dei gruppi I–II, Edizioni Cremonese (1965, 1970).Google Scholar
  14. [14]
    H. Wielandt,Finite permutation groups, Academic Press (1964).Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata (1923 -) 1978

Authors and Affiliations

  • Gabriele Korchmáros
    • 1
  1. 1.Budapest

Personalised recommendations