Abstract
Using model-theoretic methods we prove:
Theorem A
If G is a Nash group over the real or p-adic field, then there is a Nash isomorphism between neighbourhoods of the identity of G and of the set of F-rational points of an algebraic group defined over F.
Theorem B
Let G be a connected affine Nash group over ℝ. Then G is Nash isogeneous with the (real) connected component of the set of real points of an algebraic group defined over ℝ.
Theorem C
Let G be a group definable in a pseudo-finite field F. Then G is definably virtually isogeneous with the set of F-rational points of an algebraic group defined over F.
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Both authors supported by NSF grants.
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Hrushovski, E., Pillay, A. Groups definable in local fields and pseudo-finite fields. Israel J. Math. 85, 203–262 (1994). https://doi.org/10.1007/BF02758643
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DOI: https://doi.org/10.1007/BF02758643