Groups definable in linear o-minimal structures: the non-compact case

Let M = M, +, <, 0, S be a linear o-minimal expansion of an ordered group, and G = G, ⊕, eG an n-dimensional group definable in M. We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L, for some convex definable subgroup U of Mn, + and a lattice L of rank equal to the dimension of the ‘compact part’ of G.

• Type: Journal
• Year: 2010
• Where: JSYML
• Authors: Pantelis E. Eleftheriou
• Keywords: Convex Definable Subgroup, Definable Quotient Group, JSYML 2010, Linear O-minimal Expansion