2015/01/31 by Michael Braun, Michael Kiermaier, Anamari Nakić · 23 citations
Computer Science · Mathematics · Medicine · #Algorithm #Arithmetic #Automorphism #Binary number #Center (category theory) #Chronic Lymphocytic Leukemia Research #Coding theory and cryptography #Combinatorics #Conjugacy class #Crystallography #Discrete mathematics #Fano plane #Finite Group Theory Research #Geometry #Group (periodic table) #Mathematics #Order (exchange) #Physics #Plane (geometry) #Pure mathematics #math.CO
paper · pdf · doi:10.1016/j.ejc.2015.07.014
published in European Journal of Combinatorics 51, 443-457 (Elsevier BV)
arxiv created 2015/07/16 · openalex publication_date 2015/08/13 · arxiv updated 2015/10/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The smallest set of admissible parameters of a q-analog of a Steiner system is S2[2,3,7]. The existence of such a Steiner system -- known as a binary q-analog of the Fano plane -- is still open. In this article, the automorphism group of a putative binary q-analog of the Fano plane is investigated by a combination of theoretical and computational methods. As a conclusion, it is either rigid or its automorphism group is cyclic of order 2, 3 or 4. Up to conjugacy in GL(7,2), there remains a single possible group of order 2 and 4, respectively, and two possible groups of order 3. For the automorphisms of order 2, we give a more general result which is valid for any binary q-Steiner triple system.