Actions of Groups of Finite Morley Rank on Small Abelian Groups

Abstract

We classify actions of groups of finite Morley rank on abelian groups ofMorley rank 2: there are essentially two, namely the natural actions of SL(V ) and GL(V ) with V a vector space of dimension 2. We also prove an identification theorem for the natural module of SL2 in the finite Morley rank category. §