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Preprint Number 395
395. Ayse Berkman, Alexandre Borovik
Groups of Finite Morley Rank with a Pseudoreflection Action
Submission date: 16 December 2011.
In this work, we give two characterisations of the general linear group as a group G of finite Morley rank acting on an abelian connected group V of finite Morley rank definably, faithfully and irreducibly. To be more precise, we prove that if the pseudoreflection rank of G is equal to the Morley rank of V, then V has a vector space structure over an algebraically closed field, G\cong GL(V) and the action is the natural action. The same result holds also under the assumption of Prufer 2-rank of G being equal to the Morley rank of V.
Mathematics Subject Classification: 20G99, 03C60
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