Geodesic
Simple groups of Morley rank 3 are algebraic
Frécon, Olivier1
1 Laboratoire de Mathématiques et Applications, Université de Poitiers, Téléport 2 – BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France
Journal of the American Mathematical Society, Tome 31 (2018) no. 3, pp. 643-659

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

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 $K$.
DOI : 10.1090/jams/892

Frécon, Olivier 1

1 Laboratoire de Mathématiques et Applications, Université de Poitiers, Téléport 2 – BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France 
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Frécon, Olivier. Simple groups of Morley rank 3 are algebraic. Journal of the American Mathematical Society, Tome 31 (2018) no. 3, pp. 643-659. doi: 10.1090/jams/892

[1] Altä±Nel, Tuna, Borovik, Alexandre V., Cherlin, Gregory Simple groups of finite Morley rank 2008

[2] Baldwin, John T. An almost strongly minimal non-Desarguesian projective plane Trans. Amer. Math. Soc. 1994 695 711

[3] Benoist, Franck, Bouscaren, Elisabeth, Pillay, Anand On function field Mordell-Lang and Manin-Mumford J. Math. Log. 2016

[4] Borovik, A. V., Poizat, B. P. Simple groups of finite Morley rank without nonnilpotent connected subgroups 1990

[5] Borovik, Alexandre, Nesin, Ali Groups of finite Morley rank 1994

[6] Cherlin, Gregory Groups of small Morley rank Ann. Math. Logic 1979 1 28

[7] Corredor, Luis Jaime Bad groups of finite Morley rank J. Symbolic Logic 1989 768 773

[8] Hartshorne, Robin Foundations of projective geometry 1967

[9] Hrushovski, Ehud The Mordell-Lang conjecture for function fields J. Amer. Math. Soc. 1996 667 690

[10] Jaligot, Eric Full Frobenius groups of finite Morley rank and the Feit-Thompson theorem Bull. Symbolic Logic 2001 315 328

[11] Jaligot, Eric, Ould Houcine, Abderezak Existentially closed CSA-groups J. Algebra 2004 772 796

[12] Mustafin, Yerulan, Poizat, Bruno Sous-groupes superstables de 𝑆𝐿₂(𝐾) et de 𝑃𝑆𝐿₂(𝐾) J. Algebra 2006 155 167

[13] Nesin, Ali Nonsolvable groups of Morley rank 3 J. Algebra 1989 199 218

[14] Nesin, Ali On bad groups, bad fields, and pseudoplanes J. Symbolic Logic 1991 915 931

[15] Pila, Jonathan O-minimality and the André-Oort conjecture for ℂⁿ Ann. of Math. (2) 2011 1779 1840

[16] Poizat, Bruno Groupes stables 1987

[17] Poizat, Bruno Milieu et symétrie, une étude de la convexité dans les groupes sans involutions 2017

[18] Thomas, Simon The classification of the simple periodic linear groups Arch. Math. (Basel) 1983 103 116

[19] Wagner, Frank Bad groups 2017

[20] Zil′Ber, B. I. Groups and rings whose theory is categorical Fund. Math. 1977 173 188

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