On the group of units of a QWitt ring

QWitt rings are quotient rings of a special class of integral group rings for which the group is an elementary 2-group. We find the group of units of an arbitrary QWitt ring. We also find all abelian groups that can appear as the groups of units of indecomposable QWitt rings and find the way to construct a QWitt ring from a given group of units, and count all nonisomorphic SAP QWitt rings that can be constructed from the same group of units.