Abstract
A characterization of groups definable in o-minimal structures having maximal definable definably compact subgroups is given. This follows from a definable decomposition in analogy with Lie groups, where the role of maximal tori is played by maximal 0-subgroups. Along the way we give structural theorems for solvable groups, linear groups, and extensions of definably compact by torsion-free definable groups.
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