Groups of Finite Morley Rank with a Pseudoreflection Action

Details Groups of Finite Morley Rank with a Pseudoreflection Action Groups of Finite Morley Rank with a Pseudoreflection Action

2011-12-16

arxiv.org/abs/1112.3739v1

Mathematics

Group Theory

Scientific paper

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 $V$.

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