Some New Results on the Chu Duality of Discrete Groups

• Autores: Salvador Hernández Muñoz , Ta Sun Wu
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 149, Nº 3, 2006, págs. 215-232
• Idioma: inglés
• DOI: 10.1007/s00605-006-0382-z
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• Resumen

  • This paper deals mainly with the Chu duality of discrete groups. Among other results, we give sufficient conditions for an FC group to satisfy Chu duality and characterize when the Chu quasi-dual and the Takahashi quasi-dual of a group G coincide. As a consequence, it follows that when G is a weak sum of a family of finite simple groups, if the exponent of the groups in the family is bounded then G satisfies Chu duality; on the other hand, if the exponent of the group goes to infinity, then the Chu quasi-dual of G coincides with its Takahashi quasi-dual. We also present examples of discrete groups whose Chu quasi-duals are not locally compact and examples of discrete Chu reflexive groups which contain non-trivial sequences converging in the Bohr topology of the groups. Our results systematize some previous work and answer some open questions on the subject [2, 16, 3].