Revistes Catalanes amb Accés Obert (RACO)

On finite abelian groups realizable as Mislin genera

Peter Hilton, D. Scevenels


We study the realizability of finite abelian groups as Mislin genera of finitely generated nilpotent groups with finite commutator subgroup. In particular, we 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, we also give an effective way of realizing that abelian group as a genus. Further, we obtain some non-realizability results.

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