Moufang sets related to polarities in exceptional Moufang quadrangles of type F_4

Details Moufang sets related to polarities in exceptional Moufang quadrangles of type F_4 Moufang sets related to polarities in exceptional Moufang quadrangles of type F_4

2009-09-17

arxiv.org/abs/0909.3216v1

Mathematics

Group Theory

Scientific paper

Departing from a Moufang set related to a polarity in an exceptional Moufang quadrangle of type F_4, we construct a rank three geometry. The main property of this new geometry is that its automorphism group is identical to the one of the underlying Moufang set, providing a tool to study this Moufang set in a geometrical way. As a corollary we obtain that every automorphism of an exceptional Moufang quadrangle of type F_4 stabilizing the absolute points of a polarity, also centralizes the polarity. This handles the final case of a similar result for all polarities of Moufang n-gons.

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