Real Algebraic and Analytic Geometry |

Groups definable in ordered vector spaces over ordered division rings.

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Submission: 2006, January 4.

*Abstract:
Let M=(M, +, <, 0) be an ordered vector space over an
ordered division ring D, and G an n-dimensional group definable in
M. We show that if G is definably compact and definably connected
with respect to t-topology, then it is definably isomorphic to a
`definable quotient group' U/L, for some convex V-definable
subgroup U of (M^n, +) and a lattice L of rank n. As two
consequences, we derive Pillay's conjecture for M as above and we
show that the o-minimal fundamental group of G is isomorphic to L.*

Mathematics Subject Classification (2000): 03C64, 22C05, 46A40.

Keywords and Phrases: O-minimal structures, Definably compact groups, Quotient by lattice.

**Full text**, 31p.:
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