The subject of this paper is
a class of locally compact abelian (LCA) groups. Let p be a prime and let Z(p∞)
denote the group of complex pn-th roots of unity equipped with the discrete
topology. An LCA group G is called p-thetic if it contains a dense subgroup
algebraically isomorphic to Z(p∞). It is shown that a p-thetic LCA group is either
compact or is topologically isomorphic to Z(p∞). This fact leads to the
formulation of a property which characterizes the p-thetic, the monothetic, and
the solenoidal groups. Applications to some purely algebraic questions are
presented.
