Submission date: 16 December 2011.

Abstract:

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

Keywords and phrases:

Full text arXiv 1112.3739: pdf, ps.