The sequentially pure projective dimension of global groups with decomposition bases

The sequentially pure projective dimension of a global group with a decomposition basis is computed in terms of a structural property that generalizes the earlier treatment of p-local torsion groups by Fuchs and Hill. As a corollary, it is established that a global group with a decomposition basis and cardinality n, for some nonnegative integer n, has sequentially pure projective dimension not exceeding n.