Nice bases and thickness in primary Abelian groups. (Q635261)

An Abelian \(p\)-group has a nice basis if it is the union of an ascending sequence of nice \(\Sigma\)-cyclic subgroups. This notion is a generalisation of several structure theorems in the literature on Abelian groups. The authors prove several results pertaining to nice bases and Ulm subgroups. For example, they show that a separable group is thick if and only if whenever it is represented as the quotient of a group with a nice basis by its Ulm subgroup, then this Ulm subgroup is \(\Sigma\)-cyclic. The deepest results in the paper involve the assumption of the continuum hypothesis.