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Simple groups of Morley rank $ 3$ are algebraic


Author: Olivier Frécon
Journal: J. Amer. Math. Soc. 31 (2018), 643-659
MSC (2010): Primary 20F11; Secondary 03C45, 20A15
DOI: https://doi.org/10.1090/jams/892
Published electronically: November 7, 2017
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Abstract: There exists no bad group (in the sense of Gregory Cherlin); namely, any simple group of Morley rank 3 is isomorphic to $ {\rm PSL}_2(K)$ for an algebraically closed field $ K$.


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Additional Information

Olivier Frécon
Affiliation: Laboratoire de Mathématiques et Applications, Université de Poitiers, Téléport 2 – BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France
Email: olivier.frecon@math.univ-poitiers.fr

DOI: https://doi.org/10.1090/jams/892
Keywords: Groups of finite Morley rank, bad groups, projective space.
Received by editor(s): September 25, 2016
Received by editor(s) in revised form: August 6, 2017, and October 8, 2017
Published electronically: November 7, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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