Advertisement

Annali di Matematica Pura ed Applicata

, Volume 135, Issue 1, pp 151–172 | Cite as

Strutture di André edS-spazi con traslazioni: II

  • Mauro Biliotti
Article

Summary

We investigate finite André-structures and Sperner-spaces with the property that the stabilizer of a line in the traslation group is never identical. For this purpose we make use of a suitable representation of these structures by means of a set of partitions of a finite group. Results of various types are obtained, mostly in connection with collineations and constructions of new classes.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliografia

  1. [1]
    J. André,über Parallelstrukturen, Teil I:Grundbegriffe, Math. Z.,76 (1961), pp. 85–102.Google Scholar
  2. [2]
    J. André,über Parattelstrukturen, Teil II:Translationsstrukturen, Math. Z.,76 (1961), pp. 155–163.Google Scholar
  3. [3]
    J. André,über Parallelstrukturen, Teil III:Zentrale t-Strukturen, Math. Z.,76 (1961), pp. 240–256.Google Scholar
  4. [4]
    J. André,über Parallelstrukturen, Teil IV:T-Strukturen, Math. Z.,76 (1961), pp. 311–333.Google Scholar
  5. [5]
    M. Biliotti,Strutture di André ed S-spazi con traslazioni, Geom. Dedicata,10 (1981), pp. 113–128.Google Scholar
  6. [6]
    M. Biliotti -A. Scarselli,Sulle strutture di traslazione dotate di dilatazioni proprie, Atti Acc. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Nat., (8)67 (1979), pp. 75–80.Google Scholar
  7. [7]
    P. Dembowski,Finite Geometries, Springer, Berlin - Heidelberg - New York, 1968.Google Scholar
  8. [8]
    A. Herzer,Endliche nichtkommutative Gruppen mit Partition π und fixpunktfreiem π-Automorphismus, Arch. Math. (Basel),34 (1980), pp. 385–392.Google Scholar
  9. [9]
    D. R. Hughes -J. G. Thompson,The H p-problem and the structure of H p-groups, Pacific J. Math.,9 (1959), pp. 1097–1102.Google Scholar
  10. [10]
    B. Huppert,Endliche Gruppen I, Springer, Berlin - Heidelberg - New York, 1967.Google Scholar
  11. [11]
    O. Kegel,AufzÄhlung der Partitionen endlicher Gruppen mit trivialer Fittingscher Untergruppe, Arch. Math. (Basel),12 (1961), pp. 409–412.Google Scholar
  12. [12]
    P. Kontorowisch,Sur les groupes à base de partition, Mat. Sbornik,12 (1943), pp. 56–70 (in Russo).Google Scholar
  13. [13]
    E. Sperner,Affine RÄume mit schwacher Inzidenz und zugehörige algebraische Strukturen, J. Reine Angew. Math.,204 (1960), pp. 205–215.Google Scholar
  14. [14]
    M. Suzuki,A new type of simple groups of finite order, Proc. Nat. Acad. Sci. U.S.A.,46 (1960), pp. 868–870.Google Scholar
  15. [15]
    M. Suzuki,On a class of doubly transitive groups, Ann. of Math., (2)75 (1962), pp. 105–145.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1983

Authors and Affiliations

  • Mauro Biliotti
    • 1
  1. 1.Lecce

Personalised recommendations