#### Vol. 307, No. 2, 2020

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Exceptional groups of relative rank one and Galois involutions of Tits quadrangles

### Bernhard Mühlherr and Richard M. Weiss

Vol. 307 (2020), No. 2, 391–454
##### Abstract

Weshow that every Moufang set associated with one of the Tits indices ${}^{2}\phantom{\rule{-0.17em}{0ex}}{E}_{6,1}^{29}$, ${E}_{7,1}^{48}$, ${E}_{8,1}^{91}$ or ${F}_{4,1}^{21}$ in arbitrary characteristic can be obtained as the fixed point building of a Galois involution acting on a Tits quadrangle parametrized by a quadrangular algebra. This result is used to calculate an explicit formula for the structure map of an arbitrary Moufang set in this class.

##### Keywords
building, Moufang set, Tits polygon, exceptional group
##### Mathematical Subject Classification 2010
Primary: 20E42, 51E12, 51E24
##### Milestones
Received: 27 September 2019
Revised: 9 April 2020
Accepted: 26 April 2020
Published: 4 September 2020
##### Authors
 Bernhard Mühlherr Mathematisches Institut Universität Giessen Germany Richard M. Weiss Mathematics Tufts University Medford, MA United States