Submission date: 12 May 2024

Abstract:

We give a review of one of the lines in development of the theory of groups of finite Morley rank. These groups naturally appear in model theory as model-theoretic analogues of Galois groups, therefore their actions and their role as permutation groups is of primary interest. We restrict our story to the study of connected groups of finite Morley rank G acting in a definably primitive way on a set X and containing a definable abelian normal subgroup V which acts on X regularly -- the so-called primitive groups of affine type. For reasons explained in the paper, this case plays a central role in the theory.

Mathematics Subject Classification: 20F11, 03C60

Keywords and phrases:

Full text arXiv 2405.07307: pdf, ps.