On the automorphism group of the binary q-analog of the Fano plane

Titelangaben

Braun, Michael ; Kiermaier, Michael ; Nakić, Anamari:
On the automorphism group of the binary q-analog of the Fano plane.
In: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems : MTNS 2014. - Groningen : Univ. , 2014 . - S. 1402-1405
ISBN 978-90-367-6321-9

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Abstract

An S_q[t, k, v] q-Steiner system is a collection of
k-dimensional subspaces of the v-dimensional vector
space GF(q)^v over the finite field GF(q) with q elements, called blocks, such that each t-dimensional subspace of GF(q)^v is contained in exactly one block. The smallest admissible parameters for which a q-Steiner system could exist is S_2[2, 3, 7]. Up to now the issue whether q-Steiner systems with these parameters exist or not is still unsolved.

In this paper we investigate the automorphism group of a putative S_2[2, 3, 7] q-Steiner system. We conclude that
in case of existence the automorphism group is cyclic and of order at most 4.