Moufang sets related to polarities in exceptional Moufang quadrangles of type F₄

2009/09/17 by Koen Struyve, Struyve, Koen
Computer Science · Engineering · Mathematics · #51E12 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.0909.3216

openalex publication_date 2009/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Departing from a Moufang set related to a polarity in an exceptional Moufang quadrangle of type F₄, 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 F₄ 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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