The order of the automorphism group of a binary $q$-analog of the Fano plane is at most two

TL;DR

This paper proves that the automorphism group of a binary q-analog of the Fano plane can only be trivial or of order two, significantly constraining its symmetry properties.

Contribution

It establishes a strict upper bound on the automorphism group's order for binary q-analogs of the Fano plane, a previously unresolved question.

Findings

Automorphism group is either trivial or of order 2

Provides a definitive bound on automorphism group size

Clarifies symmetry properties of binary q-analogs of the Fano plane

Abstract

It is shown that the automorphism group of a binary $q$-analog of the Fano plane is either trivial or of order $2$.