Abstract
We show by group-theoretic means that the absence of the Witten SU(2) (global) anomaly for gauge groups is guaranteed by the (perturbative) triangular anomaly-free condition as long as the SU(2) gauge group is embedded in a larger simple gauge group G with the property Π4(G)=0 (Π4 is the four-dimensional homotopy group). The inverse is not true. The same method could be used to relate perturbative and global anomaly cancellation in more than four dimensions. © 1987 The American Physical Society.