Compact disconnected Moufang planes are desarguesian
The author proves the claim of the title as a corollary of the following Theorem: Every non-discrete locally compact disconnected alternative field A is associative. His first proof relies on the fact that Cayley algebras over local fields do not exist. The author gives a second interesting proof: Extending results of \textit{A. Weil} [Basic Number Theory (1967; Zbl 0176.336)] to alternative fields he uses the modular function on A to construct a 2- element-set generating A. Variants of the second proof are given, one of them using the associativity of locally finite complete alternative fields, proven by \textit{H. van Maldeghem} [J. Geom. 30, 42-48 (1987)].
modular function of an alternative field
locally compact disconnected alternative field
scientific article; zbMATH DE number 4013426
scientific article