Actions of groups of finite Morley rank on small abelian groups

Bulletin of Symbolic Logic 15 (1):70-90 (2009)
Abstract
We classify actions of groups of finite Morley rank on abelian groups of Morley 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
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