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 (P,), where P is a compact projective plane with a 16-dimensional point set, Δ is an automorphism group of P of dimension at least 35, and Δ does not fix exactly one point and one line. If Δ fixes two points and only one line, then Δ contains a 15-dimensional translation group and a compact subgroup Spin7; hence dimΔ 36. The planes are described by their coordinatizing Cartesian fields, more explicitly for dimΔ > 36.

Keywords
compact projective plane, 16-dimensional plane, Cartesian field, translation group
Mathematical Subject Classification 2010
Primary: 51H10
Milestones
Received: 5 January 2009
Accepted: 21 January 2009
Authors
Hermann Hähl
Helmut Salzmann