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If A is an elementary abelian group, let 
(A) denote the group of units, modulo torsion, of the group ring Z[A]. We study (A) by means of the composite
where C and B run over all cyclic subgroups and factor-groups, respectively. This map, γ, is known to be injective; its index, too, is known. In this paper, we determine the rank of γ tensored (over Z);with various fields. Our main result depends only on the functoriality of
