Geodesic
Proper Moufang sets with abelian root groups are special
Segev, Yoav1
1Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel
Journal of the American Mathematical Society, Tome 22 (2009) no. 3, pp. 889-908

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-09-00631-6

Segev, Yoav  1

1 Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel 
Segev, Yoav. Proper Moufang sets with abelian root groups are special. Journal of the American Mathematical Society, Tome 22 (2009) no. 3, pp. 889-908. doi: 10.1090/S0894-0347-09-00631-6
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[1] De Medts, Tom, Segev, Yoav Identities in Moufang sets Trans. Amer. Math. Soc. 2008 5831 5852

[2] De Medts, Tom, Segev, Yoav Finite special Moufang sets of even characteristic Commun. Contemp. Math. 2008 449 454

[3] De Medts, Tom, Segev, Yoav, Tent, Katrin Special Moufang sets, their root groups and their 𝜇-maps Proc. Lond. Math. Soc. (3) 2008 767 791

[4] De Medts, Tom, Tent, Katrin Special abelian Moufang sets of finite Morley rank J. Group Theory 2008 645 655

[5] De Medts, Tom, Weiss, Richard M. Moufang sets and Jordan division algebras Math. Ann. 2006 415 433

[6] Hering, Christoph, Kantor, William M., Seitz, Gary M. Finite groups with a split 𝐵𝑁-pair of rank 1. I J. Algebra 1972 435 475

[7] Mühlherr, Bernhard, Van Maldeghem, Hendrik Moufang sets from groups of mixed type J. Algebra 2006 820 833

[8] Segev, Yoav Finite special Moufang sets of odd characteristic Commun. Contemp. Math. 2008 455 475

[9] Segev, Yoav, Weiss, Richard M. On the action of the Hua subgroups in special Moufang sets Math. Proc. Cambridge Philos. Soc. 2008 77 84

[10] Timmesfeld, Franz Georg Abstract root subgroups and simple groups of Lie type 2001

[11] Timmesfeld, F. G. Quadratic rank-one groups and quadratic Jordan division algebras Proc. Lond. Math. Soc. (3) 2007 156 178

[12] Tits, Jacques Twin buildings and groups of Kac-Moody type 1992 249 286

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