Corrigenda

Carsten Eckhardt of Göttingen has pointed out that the algorithm to determine the structure of the Sylow p-subgroup Sp of the class group may only produce a subgroup of Sp. In all of the cases in which this algorithm was run we actually obtained Sp; hence, the results in Section 5 are not affected by this observation. Nevertheless, the complexity result given in the paper has not been proved. This difficulty can be overcome by first extending and improving Algorithm 4.1. We first note that we may assume that |A| is large enough so that R > 1 (see, for example, Cusick [1]). We let t)i (i = 1,2,..., k) be k reduced ideals of Ok with periods p, = p*1' (p¿ E Z), where p is a prime. We put P = p\p2 • ■ ■ pk =p>i. Given a reduced ideal j, our new algorithm will either determine i, (< pi) (i = 1,2,..., k) such that (4.1) holds or establish that no such set of í¿'s exists. This algorithm executes in 0(y/PR\A\£) elementary operations. We note that if (4.1) holds, then