Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Involutory incidence spaces

  • 23 Accesses

  • 2 Citations

Abstract

Recently H. Karzel gave a characterisation of reflection groups by group spaces. We obtain new geometries by replacing one of the axioms by its negation. An algebraic description of these geometries is given.

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

References

  1. [1]

    ELLERS, E. and H. KARZEL: Involutorische Geometrien. Abh. Math. Sem. Univ. Hamburg 25, 93–104 (1961).

  2. [2]

    ELLERS, E. and H. KARZEL: Kennzeichnung elliptischer GruppenrÄume. Abh. Math. Sem. Univ. Hamburg 26, 55–77 (1963).

  3. [3]

    KARZEL, H.: Verallgemeinerte elliptische Geometrien und ihre GruppenrÄume. Abh. Math. Sem. Univ. Hamburg 24, 167–188 (1960).

  4. [4]

    KARZEL, H.: Bericht über projektive Inzidenzgruppen. Jahresber. d. DMV. 67, 58–92 (1964).

  5. [5]

    KARZEL, H.: Spiegelungsgruppen und absolute GruppenrÄume. Abh. Math. Sem. Univ. Hamburg 35, 141–163 (1971).

  6. [6]

    KARZEL, H. and H. MEISSNER: Geschlitzte Inzidenzgruppen und normale Fastmoduln. Abh. Math. Sem. Univ. Hamburg 31, 69–88 (1967).

  7. [7]

    MEISSNER, H.: Geschlitzte GruppenrÄume. Abh. Math. Sem. Univ. Hamburg 32, 160–185 (1968).

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ellers, E., Karzel, H. Involutory incidence spaces. J Geom 1, 117–126 (1971). https://doi.org/10.1007/BF02150266

Download citation

Keywords

  • Reflection Group
  • Algebraic Description
  • Incidence Space