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
MathSciNet review:
3787404
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View in AMS MathViewer
Abstract | References | Similar Articles | Additional Information
Abstract: There exists no bad group (in the sense of Gregory Cherlin); namely, any simple group of Morley rank 3 is isomorphic to $\textrm {PSL}_2(K)$ 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
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