Journal of Geometry

, Volume 105, Issue 2, pp 391–417 | Cite as

The configurations 123 revisited

  • Abdullah Al-Azemi
  • Dieter Betten


As is known, there are 229 symmetric configurations 123, (Daublebsky von Sterneck in Monatshefte Math Phys 5:223–255, 1895; Gropp in J Comb Inf Syst Sci 15:34–48, 1990). We use tactical decompositions by automorphism group (TDA) to study these configurations in detail. In (Daublebsky von Sterneck in Monatshefte Math Phys 14, 254–260, 1903) the automorphism groups of the configurations were determined. We find some errors there and correct them. For the configurations with a rather big automorphism group, we give models which display the structure of the group.

Mathematics Subject Classification (2010)

05E18 05XX 


Configurations tactical decompositions linear spaces 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Abdullah Al-Azemi
    • 1
  • Dieter Betten
    • 2
  1. 1.Department of Mathematics, Faculty of ScienceKuwait UniversitySafatKuwait
  2. 2.Math. Seminar Univ. KielKielGermany

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