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This research investigates the relationship between definably primitive pseudo-finite permutation groups and their ranks.

June 18, 2026

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Primitive pseudo-finite permutation groups of finite 𝑆𝑈-rank

UKUlla KarhumäkiUniversité Claude Bernard Lyon 1 NRNicholas RamseyUniversity of Notre Dame

Key Points

This research investigates the relationship between definably primitive pseudo-finite permutation groups and their ranks.
Analyzed the properties of permutation groups defined by (G,X)
Established bounds on the rank of G in relation to the rank of X
Provided an analogy with existing theorems in the context of finite Morley rank.
Found that the rank of G can indeed be bounded by the rank of X.
Demonstrated a structural similarity to Borovik and Cherlin's theorem.
Identified implications for the classification of permutation groups.

Abstract

We study definably primitive pseudo-finite permutation groups of finite S U SU -rank. We show that if ( G , X ) (G,X) is such a permutation group, then the rank of G G can be bounded in terms of the rank of X X , providing an analogue of a theorem of Borovik and Cherlin in the setting of definably primitive permutation groups of finite Morley rank.

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Primitive pseudo-finite permutation groups of finite 𝑆𝑈-rank

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