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Proper Moufang sets with abelian root groups are special


Author: Yoav Segev
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
Published electronically: January 5, 2009
MathSciNet review: 2505304
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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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Additional Information

Yoav Segev
Affiliation: Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel
Email: yoavs@math.bgu.ac.il

DOI: https://doi.org/10.1090/S0894-0347-09-00631-6
Keywords: Moufang set, root group
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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