Innovations in Incidence Geometry

A course on Moufang sets

Tom De Medts and Yoav Segev

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A Moufang set is essentially a doubly transitive permutation group such that the point stabilizer contains a normal subgroup which is regular on the remaining points. These regular normal subgroups are called the root groups and they are assumed to be conjugate and to generate the whole group.

Moufang sets play an significant role in the theory of buildings, they provide a tool to study linear algebraic groups of relative rank one, and they have (surprising) connections with other algebraic structures.

In these course notes we try to present the current approach to Moufang sets. We include examples, connections with related areas of mathematics and some proofs where we think it is instructive and within the scope of these notes.

Article information

Innov. Incidence Geom., Volume 9, Number 1 (2009), 79-122.

Received: 25 June 2007
Accepted: 7 November 2007
First available in Project Euclid: 28 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17C30: Associated groups, automorphisms 20B22: Multiply transitive infinite groups 20E42: Groups with a $BN$-pair; buildings [See also 51E24] 20G15: Linear algebraic groups over arbitrary fields 51E24: Buildings and the geometry of diagrams

Moufang sets BN-pairs rank one groups algebraic groups Jordan algebras


De Medts, Tom; Segev, Yoav. A course on Moufang sets. Innov. Incidence Geom. 9 (2009), no. 1, 79--122. doi:10.2140/iig.2009.9.79.

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