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Preprint Number 97

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97. Tuna Altinel and Jeffrey Burdges
On analogies between algebraic groups and groups of finite Morley rank

Submission date: 7 November 2007


We prove several results concerning ``Weyl groups'' of a connected group G of finite Morley rank. Here ``Weyl groups'' refers to the normalizer of a p-torus T modulo the centralizer of T. Our first result is that the centralizer of T is itself connected. Our later results use constraints on connected subgroups to limit the structure of the Weyl group; in particular minimal connected simple groups have metacyclic Weyl groups. We also show that such Weyl groups tend to be trivial in the presence of outer p-tori of automorphisms.

Mathematics Subject Classification: 03C60, 20G99

Keywords and phrases: Weyl group, simple group, Morley rank

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