Revistes Catalanes amb Accés Obert (RACO)

On finite abelian groups realizable as Mislin genera

Peter Hilton, D. Scevenels
DOI: 37910


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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