Permutation groups on countable vector spaces over prime fields

2021/12/09 by Bertalan Bodor, Michael Pinsker, Bodor, Bertalan +5
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2112.05229

openalex publication_date 2021/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe all closed permutation groups which act on the set of vectors of a countable vector space V over a prime field of odd order and which contain all automorphisms of V. In particular, we prove that their number is finite. These groups correspond, up to first-order interdefinability, precisely to all structures with a first-order definition in V.

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