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On the localization genus of a direct product of metacyclic groups
For groups H of the type G(n; u) × G(m; u) we determine the set χ(H) of all isomorphism classes of groups K with the property that K × ℤ ≅ H × ℤ. The set χ(H) carries a certain group structure which coincides with the Hilton–Mislin genus group structure …