G-linear sets and torsion points in definably compact groups

Details G-linear sets and torsion points in definably compact groups G-linear sets and torsion points in definably compact groups

2007-08-03

arxiv.org/abs/0708.0532v1

Mathematics

Logic

17 pages

Scientific paper

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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