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Journal of the London Mathematical Society Advance Access originally published online on May 14, 2008
Journal of the London Mathematical Society 2008 78(1):213-232; doi:10.1112/jlms/jdn025
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© 2008 London Mathematical Society

On analogies between algebraic groups and groups of finite Morley rank

Tuna Altinel and Jeffrey Burdges

Université de Lyon
Université Lyon 1
CNRS UMR 5208 Institut Camille Jordan
43 Boulevard du 11 novembre 1918
69622 Villeurbanne cedex
France

We prove that in a connected group of finite Morley rank the centralizers of decent tori are connected. We then apply this result to the analysis of minimal connected simple groups of finite Morley rank. Our applications include general covering properties by Borel subgroups, the description of Weyl groups and the analysis of toral automorphisms.

The second author is supported by NSF postdoctoral fellowship DMS-0503036 and a Bourse Chateaubriand postdoctoral fellowship and partially by the ANR project ‘Groupes, Géométrie et Logique’ JC05 47037: jaligot:eric:

2000 Mathematics Subject Classification 03C60, 20D05, 20G20, 20G40.

Received May 15, 2007; revised March 11, 2008; published online May 14, 2008.


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