On the quasi-component of pseudocompact abelian groups

In this paper, we describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component of its completion. Specifically, we characterize the pairs (C,A) of compact connected abelian groups C and subgroups A such that A≅q(G) and . As a consequence, we show that for every positive integer n or n=ω, there exist plenty of abelian pseudocompact perfectly minimal n-dimensional groups G such that the quasi-component of G is not dense in the quasi-component of the completion of G.