Convergent sequences in iterated ultrapowers as p-compact groups

Abstract

We prove, in ZFC, that if G is an infinite countable Abelian group, then there is an ultrafilter p∈ω⁎ such that (Ultp(G),τBohr‾) has non-trivial convergent sequences, consequently (Ultpω1(G),τBohr‾) has non-trivial convergent sequences, extending Theorem 3.9 from [13]. In addition, we prove that the Remark 3.8 from [13] is false; so, the proof of the Corollary 3.11 is false too.