The computation of the projective surgery obstruction groups LP.(ZG), for G a hyperelementary finite group, is reduced to standard calculations in number theory, mostly involving class groups. Both the exponent of the torsion subgroup and the precise divisibility of the signatures are determined. For G a 2-hyperelementary group, the LP.(ZG) are detected by restriction to certain subquotients of G, and a complete set of invariants is given for oriented surgery obstructions
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