Chains of pseudocompact group topologies

We show that for several large classes of groups G, the poset P-sigma(G) of all pseudocompact group topologies of weight sigma on G contains a poset isomorphic to the power set of sigma whenever P-sigma(G) not equal theta. This permits to describe in purely set-theoretic terms when G has bounded (from above) chains of pseudocompact group topologies of weight sigma. Moreover, we show that these topologies may additionally have some of the following properties: linear (in particular, zero-dimensional), connected and locally connected, disconnected and locally connected, connected and nonlocally connected, etc. It turns out that the question of whether the cardinality of unbounded chains of pseudocompact group topologies of weight omega(1) on R is larger than that of bounded ones cannot be answered in ZFC. We answer also questions posed by Comfort and Remus (1994) on pseudocompact topologization of a given weight. (C) 1998 Elsevier Science B.V.