The order of the automorphism group of a binary \({\varvec{q}}\)-analog of the Fano plane is at most two

  • Michael Kiermaier
  • Sascha Kurz
  • Alfred Wassermann
Article
Part of the following topical collections:
  1. Special Issue on Network Coding and Designs

Abstract

The question if there exists a q-analog of the Fano plane is open since it was first posed in 1972. For a putative binary q-analog of the Fano plane all automorphisms of order greater than 4 had been excluded previously. Here, it is shown with theoretical and computational methods that the order of the automorphism group of a binary q-analog of the Fano plane is either trivial or of order 2. Moreover, some groups which had been excluded by computer search in Braun et al. (Eur J Comb 51:443–457, 2016) are ruled out as automorphism group by theoretic arguments.

Keywords

Steiner triple systems q-Analogs of designs Fano plane Automorphism group 

Mathematics Subject Classification

51E20 05B07 05A30 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität BayreuthBayreuthGermany

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