Meinem verehrten Lehrer Helmut Salzmann zum 60. Geburtstag
ABSWRACT. New results of Salzmann and Hubig say that a 16-dimensional (locally) compact topological projective plane in which the group (3 of continuous collineations has dimension >740 is a translation plane. It is therefore important to determine all 16-dimensional locally compact translation planes with dim G ~> 40. From previous work of the author ([10]), it is known that such a plane is either the classical octonion plane, or dim G = 40 and G contains a subgroup isomorphic to the compact exceptional group G2, but no larger compact simple subgroup. In the present paper, all planes satisfying the latter property more generally with dim G/> 38 are explicitly determined. Together with the classification of all 16-dimensional locally compact translation planes in which G contains Spin(7) given by the author in [8], one thus knows all 16-dimensional locally compact translation planes with G containing G 2 and dim G >~ 38. Via suitable Baer subplanes, the classification makes use of analogous results for 8dimensional planes (I-7]).
EINLEITUNG