G-linear sets and torsion points in definably compact groups

Margarita Otero; Ya'acov Peterzil

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arXiv · 0708.0532

G-linear sets and torsion points in definably compact groups

Margarita Otero·Ya'acov Peterzil

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Abstract

Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G X) < dim G for some definable X subset of G then X contains a torsion point of G. Along the way we develop a general theory for so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.

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BibTeX RIS

Margarita Otero, Ya'acov Peterzil. 2007-08-03. G-linear sets and torsion points in definably compact groups. https://arxiv.org/abs/0708.0532

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