Abstract
We examine Weyl groups of minimal connected simple groups of finite Morley rank of degenerate type. We show that they are cyclic, and lift isomorphically to subgroups of the ambient group.
Similar content being viewed by others
References
T. Altınel and J. Burdges, On analogies between algebraic groups and groups of finite Morley rank, The Journal of the London Mathematical Society 78 (2008), 213–232.
T. Altınel, A. Borovik and G. Cherlin, Simple Groups of Finite Morley Rank, Mathematical Monographs, American Mathematical Society, Providence, RI, 2008.
A. Borovik, J. Burdges and G. Cherlin, Involutions in groups of finite Morley rank of degenerate type, Selecta Mathematica 13 (2007), 1–22.
J. Burdges and G. Cherlin, A generation theorem for groups of finite Morley rank, The Journal of Mathematical Logic, 2010, to appear.
J. Burdges and G. Cherlin, Semisimple torsion in groups of finite Morley rank, 2010, submitted.
J. Burdges, G. Cherlin and E. Jaligot, Minimal connected simple groups of finite Morley rank with strongly embedded subgroups, Journal of Algebra 314 (2007), 581–612.
A. Baudisch, M. Hils, A. Martin-Pizarro and F. O. Wagner, Die Böse Farbe, Journal of the Institute of Mathematics of Jussieu 8 (2009), 415–443.
A. Borovik and A. Nesin, Groups of Finite Morley Rank, The Clarendon Press Oxford University Press, New York, 1994.
J. Burdges, Simple Groups of Finite Morley Rank of Odd and Degenerate Type, PhD thesis, Rutgers University, 2004.
J. Burdges, A signalizer functor theorem for groups of finite Morley rank, Journal of Algebra 274 (2004), 215–229.
J. Burdges, The Bender method in groups of finite Morley rank, Journal of Algebra 312 (2007), 33–55.
J. Burdges, Signalizers and balance in groups of finite Morley rank, Journal of Algebra 321 (2009), 1383–1406.
G. Cherlin, Good tori in groups of finite Morley rank, Journal of Group Theory 8 (2005), 613–621.
G. Cherlin and E. Jaligot, Tame minimal simple groups of finite Morley rank, Journal of Algebra 276 (2004), 13–79.
A. Deloro, Groupes Simples Connexes Minimaux de Type Impair, PhD thesis, Université Paris 7, Paris, 2007.
A. Deloro, Groupes simples connexes minimaux algébriques de type impair, Journal of Algebra 317 (2007), 877–923.
A. Deloro, Groupes simples connexes minimaux non-algébriques de type impair, Journal of Algebra 319 (2008), 1636–1684.
O. Frécon, Around unipotence in groups of finite Morley rank, Journal of Group Theory 9 (2006), 341–359.
O. Frécon, Conjugacy of Carter subgroups in groups of finite Morley rank, The Journal of Mathematical Logic 8 (2008), 41–92.
D. Gorenstein, Finite groups, second edition, Chelsea Publishing Co., New York, 1980.
E. Hrushovski and F. Wagner, Counting and dimensions, in Model Theory with Applications to Algebra and Analysis, Vol. 2, London Mathematical Society Lecture Note Series, Vol. 350, Cambridge University Press, Cambridge, 2008, pp. 161–176.
E. Jaligot and O. Frécon, Conjugacy in groups of finite Morley rank, UPRESA 5028(33), Janvier 2000/n.
F. O. Wagner, Stable Groups, Cambridge University Press, Cambridge, 1997.
F. Wagner, Fields of finite Morley rank, The Journal of Symbolic Logic 66 (2001), 703–706.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by NSF postdoctoral fellowship DMS-0503036.
Rights and permissions
About this article
Cite this article
Burdges, J., Deloro, A. Weyl groups of small groups of finite Morley rank. Isr. J. Math. 179, 403–423 (2010). https://doi.org/10.1007/s11856-010-0087-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11856-010-0087-9