On decomposable pseudofree groups.
On the Mislin genus of certain circle bundles and noncancellation.
On the existence of group localizations under large-cardinal axioms.
Uno de los problemas abiertos más antiguos de la teoría de grupos categórica es si todo par ortogonal (formado por una clase de grupos y una clase de homomorfismos que se determinan mutuamente por ortogonalidad en el sentido de Freyd-Kelly), se halla asociado a un funtor de localización. Se sabe que esto es cierto si se acepta la validez de un cierto axioma de cardinales grandes (el principio de Vopenka), pero no se conoce ninguna demostración mediante los axiomas ordinarios (ZFC) de la teoría de...
Calculating the genus of a direct product of certain nilpotent groups.
The Mislin genus G(N) of a finitely generated nilpotent group N with finite commutator subgroup admits an abelian group structure. If N satisfies some additional conditions -we say that N belongs to - we know exactly the structure of G(N). Considering a direct product N x ... x N of groups in takes us virtually always out of . We here calculate the Mislin genus of such a direct product.
On finite abelian groups realizable as Mislin genera.
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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