Abstract.
The well-known finite Hughes planes have compact analoga with 16-dimensional point space. The automorphism group of such a plane is a 36-dimensional Lie group. Theorem: Assume that the compact projective plane $\cal P $ is not isomorphic to the classical Moufang plane over the octonions. Let $\Delta $ be a closed subgroup of $\hbox {Aut} \,\cal P $ . If $\dim \Delta \ge 31$ and if $\Delta $ has a normal torus subgroup, then $\cal P $ is a Hughes plane, $\Delta = \hbox {Aut} \,\cal P $ , and $\Delta ^{\prime } \cong \hbox {PSL}_3 \Bbb H $ .
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Received: 19.8.1997
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Salzmann, H. Characterization of 16-dimensional Hughes planes. Arch. Math. 71, 249–256 (1998). https://doi.org/10.1007/s000130050261
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DOI: https://doi.org/10.1007/s000130050261