Permutation groups on countable vector spaces over prime fields

Bertalan Bodor; Michael Pinsker; Lyra Schiffer; Csaba Szabó

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arXiv · 2112.05229

Permutation groups on countable vector spaces over prime fields

Bertalan Bodor·Michael Pinsker·Lyra Schiffer·Csaba Szabó

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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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BibTeX RIS

Bertalan Bodor, Michael Pinsker, Lyra Schiffer, Csaba Szabó. 2021-12-09. Permutation groups on countable vector spaces over prime fields. https://arxiv.org/abs/2112.05229

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