Primitive permutation groups of finite Morley rank and affine type

2024/05/12 by Ayşe Berkman, Berkman, Ayşe, Alexandre Borovik +1
Mathematics · #03C60 #20F11 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2405.07307

openalex publication_date 2024/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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