Designs, Codes and Cryptography

, Volume 44, Issue 1–3, pp 217–221 | Cite as

Finite structures with prescribed numbers of orbits of their automorphism group

  • Anne Delandtsheer
  • Jean Doyen


We discuss the problem of existence of finite structures (groups, linear spaces, graphs, ...) with prescribed numbers of orbits of their automorphism groups on the various types of elements.


Orbits Automorphism groups 

AMS Classifications

20B25 20D45 


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  1. 1.
    Block RE (1967). On the orbits of collineation groups. Math Z 96: 33–49 MATHCrossRefGoogle Scholar
  2. 2.
    Blokhuis A, Brouwer A, Delandtsheer A and Doyen J (1987). Orbits on points and lines in finite linear and quasilinear spaces. J Combin Theory Ser A 44: 159–163 MATHCrossRefGoogle Scholar
  3. 3.
    Bougard N. Orbits on vertices and edges in finite regular graphs (to appear)Google Scholar
  4. 4.
    Bougard N (2007). Orbits in finite regular graphs. Euro J Combin 28: 439–456 MATHCrossRefGoogle Scholar
  5. 5.
    Buekenhout F (1964). Les plans d’André finis de dimension quatre sur le noyau. Acad Roy Belg Bull Cl Sci 50: 446–457 Google Scholar
  6. 6.
    Buset D (1985). Orbits on vertices and edges of finite graphs. Discrete Math 57: 297–299 MATHCrossRefGoogle Scholar
  7. 7.
    Delandtsheer A (1986). Orbits in uniform hypergraphs. Discrete Math 61: 317–319 MATHCrossRefGoogle Scholar
  8. 8.
    Dixon JD (1967). Problems in group theory. Blaisdell, Waltham MATHGoogle Scholar
  9. 9.
    Gorenstein D (1968). Finite groups. Harper and Row, New York MATHGoogle Scholar
  10. 10.
    Hall M (1964). The theory of groups. Macmillan, New York MATHGoogle Scholar
  11. 11.
    Hughes DR (1957). A class of non-Desarguesian projective planes. Can J Math 9: 378–388 MATHGoogle Scholar
  12. 12.
    Kochendörffer R (1970). Group theory. McGraw-Hill, Maidenhead MATHGoogle Scholar
  13. 13.
    Passman DS (1968). Permutation groups. Benjamin, New York MATHGoogle Scholar
  14. 14.
    Royle G. http:// (see combinatorial data, translation planes of order 49)Google Scholar
  15. 15.
    Saxl J (1981). On points and triples of Steiner triple systems. Arch Math 36: 558–564 MATHCrossRefGoogle Scholar
  16. 16.
    Suzuki M. Group theory. Springer-Verlag, Berlin, 1982 (Vol. I) and 1986 (Vol. II)Google Scholar
  17. 17.
    Tsuzuku T (1982) Finite groups and finite geometries. Cambridge Univ. PressGoogle Scholar
  18. 18.
    Bensaid A and Waall RW (1991). On finite goups whose elements of equal order are conjugate. Simon Stevin 65: 361–374 Google Scholar
  19. 19.
    Zhang J (1992). On finite groups all of whose elements of the same order are conjugate in their automorphism groups. J Algebra 153: 22–36 MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Faculté des Sciences Appliquées, Service de MathématiquesUniversité Libre de BruxellesBruxellesBelgium
  2. 2.Faculté des Sciences, Service de GéométrieUniversité Libre de BruxellesBruxellesBelgium

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