Identities valid globally in semigroups.
The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, . We show: Theorem 4.12. Let G be Abelian with |G| = γ. If either m(α) ≤ α and m, or α > ω and , then G admits a pseudocompact group topology of weight α. Theorem 4.15. Every connected, pseudocompact Abelian group G with wG = α ≥ ω satisfies . Theorem 5.2(b). If G is divisible Abelian with , then G admits at most -many...
Almost completely decomposable groups with a critical typeset of type and a -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient , either no indecomposables if ; only six near isomorphism types of indecomposables if ; and indecomposables of arbitrary large rank if .