#### Vol. 11, No. 1, 2010

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16-dimensional compact projective planes with a large group fixing two points and only one line

### Hermann Hähl and Helmut Salzmann

Vol. 11 (2010), No. 1, 213–235
DOI: 10.2140/iig.2010.11.213
##### Abstract

We complete the determination of all pairs $\left(\mathsc{P},\cdot \right)$, where $\mathsc{P}$ is a compact projective plane with a $16$-dimensional point set, $\Delta$ is an automorphism group of $\mathsc{P}$ 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 ${Spin}_{7}ℝ$; hence $dim\Delta \ge 36$. The planes are described by their coordinatizing Cartesian fields, more explicitly for $dim\Delta >36$.

##### Keywords
compact projective plane, 16-dimensional plane, Cartesian field, translation group
Primary: 51H10
##### Milestones
Received: 5 January 2009
Accepted: 21 January 2009
##### Authors
 Hermann Hähl Helmut Salzmann