Abstract:Moufang sets are split $BN$-pairs of rank one, or the Moufang buildings of rank one. As such they have been studied extensively, being the basic ‘building blocks’ of all split $BN$-pairs. A Moufang set is proper if it is not sharply $2$-transitive. We prove that a proper Moufang set whose root groups are abelian is special. This resolves an important conjecture in the area of Moufang sets. It enables us to apply the theory of quadratic Jordan division algebras to such Moufang sets.
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- Yoav Segev
- Affiliation: Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel
- MR Author ID: 225088
- Email: firstname.lastname@example.org
- Received by editor(s): February 19, 2008
- Published electronically: January 5, 2009
- Additional Notes: The author was partially supported by BSF grant no. 2004-083
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: J. Amer. Math. Soc. 22 (2009), 889-908
- MSC (2000): Primary 20E42; Secondary 17C60
- DOI: https://doi.org/10.1090/S0894-0347-09-00631-6
- MathSciNet review: 2505304