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

Published electronically:
January 5, 2009

MathSciNet review:
2505304

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Abstract: Moufang sets are split -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 -pairs. A Moufang set is proper if it is not sharply -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:
http://dx.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.