On finite Abelian groups realizable as Mislin genera
The Mislin genus of a finitely generated nilpotent group \(N\) is the set of isomorphism classes of finitely generated nilpotent groups \(M\) having, at each prime \(p\), a localization isomorphic with that of \(N\), i.e. \(M_p\cong N_p\) for all \(p\). The authors study the realizability of finite Abelian groups as Mislin genera of finitely generated nilpotent groups with finite commutator subgroup. In particular, they give criteria to decide whether a finite Abelian group is realizable as the Mislin genus of a direct product of nilpotent groups of a certain specified type. In the case of a positive answer, the authors give an effective way of realizing that Abelian group as a genus. Further, some non-realizability results are obtained.
scientific article; zbMATH DE number 1146199