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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W. / Wilson, John S.

Managing Editor: Khukhro, Evgenii I. / Kramer, Linus

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Special abelian Moufang sets of finite Morley rank

Tom De Medts1 / Katrin Tent2

1Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, 9000 Gent, Belgium. E-mail: tdemedts@cage.UGent.be

2Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany. E-mail: ktent@math.uni-bielefeld.de

Citation Information: Journal of Group Theory. Volume 11, Issue 5, Pages 645–655, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/JGT.2008.040, September 2008

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Moufang sets are split doubly transitive permutation groups, or equivalently, groups with a split BN-pair of rank one. In this paper, we study so-called special Moufang sets with abelian root groups, under the model-theoretic restriction that the groups have finite Morley rank. These groups have a natural base field, and we classify them under the additional assumption that the base field is infinite. The result is that the group is isomorphic to PSL2(K) over some algebraically closed field K.

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