A class of monothetic reflexive groups and the Weil property (Q6629186)

The article is separated into two parts. Being motivated by a result of Weil, in the first one the author introduces and studies the (strong) Weil property: an abelian group is said to have the (strong) Weil property if every cyclic subgroup is either discrete or precompact (resp., each finitely generated subgroup is locally precompact). Some permanent properties are studied: the class of groups with the (strong) Weil property is closed under taking arbitrary products and subgroups, and every abelian Hausdorff group is a quotient of a group with the strong Weil property. In the second part, the author studies monothetic groups which have\do not have the Weil property. In particular, it is shown that (1) there are reflexive groups which do not have the Weil property, and (2) there are abelian groups with the Weil property but without the strong Weil property and that the completion of those groups do not have the Weil property.\N\NFor the entire collection see [Zbl 1531.46002].