Extremal pseudocompact topological groups

Let P be the class of non-metrizable, pseudocompact Abelian groups. The authors contribute to the growing literature (see for example J. Galindo, Sci. Math. Japonicae 55 (2001) 627) supporting the conjecture that no G∈P is either r- nor s-extremal-but that conjecture remains open. Except for portions of (a), the following are new results concerning G∈P proved here. The proofs derive largely from basic, sometimes subtle, considerations comparing the algebraic structure of G∈P with the algebraic structure of the Weil completion G¯. (a) If G is either r- or s-extremal, then r0(G)=c