[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

Subregular planes admitting elations

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

New classes of subregular planes are constructed that admit elation groups or Baer groups of order > 2. Further, we construct a variety of large dimension translation planes admitting many elations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abatangelo V, Larato B (1986) Translation planes with an automorphism group isomorphic to SL(2,5). Ann Discrete Math 30:1–8

    MATH  MathSciNet  Google Scholar 

  2. Albert AA (1966) The finite planes of Ostrom. Bol Soc Mat Mex 11(2):1–13

    MATH  MathSciNet  Google Scholar 

  3. Biliotti M, Jha V, Johnson NL (2001) Foundations of translation planes. Pure and applied Mathematics, vol 243. Marcel Dekker, New York, Basel, pp 1–552

  4. Bonisoli A, Korchmáros G, Szönyi T (1997) Some multiply derived translation planes with SL(2,5) as an inherited collineation group in the translation complement. Design Code Crypogr 10:109–114

    Article  MATH  Google Scholar 

  5. Bruck RH (1970) Construction problems of finite projective planes. Conference on Combinatorial Mathematics and its Applications (University of North Carolina, 1967), University of North Carolina Press, Chapel Hill, NC, pp 426–514

  6. Charnes C, Dempwolff U (1995) Spreads, ovoids and S 5. Geom Ded 56:129–143

    Article  MATH  MathSciNet  Google Scholar 

  7. Ebert GL (1977) Disjoint circles: a classification. Trans Amer Math Soc 232:83–109

    Article  MATH  MathSciNet  Google Scholar 

  8. Ebert GL (1978) Translation Planes of order q 2: asymptotic estimates. Trans Amer Math Soc 238: 301 308

    Google Scholar 

  9. Foulser DA (1973) Derived translation planes admitting affine elations. Math Z 131:183–188

    Article  MATH  MathSciNet  Google Scholar 

  10. Foulser DA (1969) Collineation groups of generalized André planes. Can J Math 21:358–369

    MATH  MathSciNet  Google Scholar 

  11. Hirschfeld JWP (1985) Finite projective spaces of three dimensions, oxford mathematical monographs. Clarendon Press, Oxford

    Google Scholar 

  12. Jha V, Johnson NL (2003) The classification of spreads in PG(3,q) admitting linear groups of order q(q + 1), II. Even Order. Adv in Geom S271–S313

  13. Johnson NL, Pomareda R, Wilke FW (1991) j-planes. J Comb Theory (ser A) 56(2):271–284

    Article  MATH  MathSciNet  Google Scholar 

  14. Johnson NL, Seydel RE (1974) A class of translation planes of order 36. Math Z 135:271–278

    Article  MATH  MathSciNet  Google Scholar 

  15. Orr WF (1976) A characterization of subregular spreads in finite 3-space. Geom Dedicata 5:43–50

    Article  MATH  MathSciNet  Google Scholar 

  16. Ostrom TG (1970) Translation planes admitting homologies of large order. Math Z 114:79–92

    Article  MATH  MathSciNet  Google Scholar 

  17. Ostrom TG (1970) A class of translation planes admitting elations which are not translations. Arch Math 21:214–217

    Article  MATH  MathSciNet  Google Scholar 

  18. Prohaska O (1977) Konfigurationen einander meidender Kreise in miquelschen Möbiusebenen ungerader Ordnung. Arch Math. (Basel) 28(5):550–556

    MATH  MathSciNet  Google Scholar 

  19. Thas JA (1973) Flocks of finite egglike inversive planes. In: Barlotti A, (ed) (1973). Finite geometric structures and their applications, Bressanone 1972. Cremonese, Roma, pp 189–191

  20. Walker M (1976) The collineation groups of derived translation planes II. Math Z 148(1):1–6

    Article  MATH  MathSciNet  Google Scholar 

  21. Walker M (1976) The collineation groups of derived translation planes. Geometriae Dedicata 5:87–95

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vikram Jha.

Additional information

communicated by M.J. de Resmini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jha, V., Johnson, N.L. Subregular planes admitting elations. Des Codes Crypt 41, 125–145 (2006). https://doi.org/10.1007/s10623-006-9001-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-006-9001-1

Keywords

AMS Classifications

Navigation