Primitive pseudo-finite permutation groups of finite 𝑆𝑈-rank

Ulla Karhumäki; Nicholas Ramsey

doi:10.1090/tran/9690

June 16, 2026Transactions of the American Mathematical Society

Primitive pseudo-finite permutation groups of finite 𝑆𝑈-rank

View at Publisher

Ask AI

Bookmark

Share

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.

Implication

Examines the properties of pseudo-finite permutation groups, suggesting a link to the Morley rank.

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.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Karhumäki et al. (2026) studied this question.

synapsesocial.com/papers/6a338e14630953a74978ed22 https://doi.org/10.1090/tran/9690

View at Publisher

Ask AI

Bookmark

Share

Primitive pseudo-finite permutation groups of finite 𝑆𝑈-rank

Key Points

Implication

Abstract

Discussion

Cite This Study

Primitive pseudo-finite permutation groups of finite 𝑆𝑈-rank

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading