Abstract

We complete the determination of all pairs $\left(\mathcal{P},\cdot \right)$, where $\mathcal{P}$ is a compact projective plane with a $16$-dimensional point set, $\Delta$ is an automorphism group of $\mathcal{P}$ of dimension at least $35$, and $\Delta$ does not fix exactly one point and one line. If $\Delta$ fixes two points and only one line, then $\Delta$ contains a $15$-dimensional translation group and a compact subgroup ${Spin}_7ℝ$; hence $dim\Delta \ge 36$. The planes are described by their coordinatizing Cartesian fields, more explicitly for $dim\Delta >36$.

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Mathematical Subject Classification 2010

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