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Let $G$ be an ordered group that is a direct sum of a rank-one torsion-freeabelian group and a finite-rank torsion-free abelian group, with orderstructure arising from the natural order on the first summand. A necessarycondition and a sufficient condition are given for $G$ to have an ordered-groupinductive limit representation using injective maps.

The ultrasimplicial property for simple dimension groups with unique state, the image of which has rank one