A central decomposition of connected groups of finite Morley rank
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Rachad Bentbib
and
Olivier Frécon
Abstract
We introduce a simple equivalence relation on strongly minimal sets in a structure of finite Morley rank, which corresponds, in stability theory, to the non-orthogonality of the associated types.
We use it in a group 𝐺 of finite Morley rank to define, for each strongly minimal set 𝑋, two connected normal subgroups
Acknowledgements
The authors would like to thank Frank O. Wagner for clarifying a technical point related to stability theory. They would also like to thank the referees for their remarks which improved this paper. The bulk of this work was done when R. Bentbib was a PhD student affiliated with the same organization as O. Frécon.
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Communicated by: Evgenii I. Khukhro
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