Removing the torsion from a unital group

We review the relationships among unital groups, physical systems, observables, symmetries, and states and ponder about the interpretation of the torsion subgroup in this context. If G is a unital group and Gτ is the torsion subgroup of G, then by forming the quotient group H=GGτ we can “remove the torsion” from G. If G is R-unital, then H can be organized into an R-unital group in such a way that G and H have the same state space. If G has a finite unit interval, then Gτ is a finite group, H has a finite unit interval, H can be identified (as a group) with Zr, and G is isomorphic (as a group) to H × Gr. Every torsion-free Z-unital group H with a finite unit interval can be obtained in this way by removing the torsion from a unigroup G with a finite unit interval, whence a torsion-free Z-unital group with a finite unit interval is R-unital.