On transversal group topologies

Reflexive Group Topologies on Abelian Groups

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology. Introduction For a topological group G, the group G of continuous homomorphisms (characters) into the torus T = {z ∈ C : |z| = 1} endowed with the compact-open topology is called the character group of G and G is named Pontryagin reflexive or reflexive if the canonical homomorphism ...

Imposing pseudocompact group topologies on Abelian groups

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, m(α) ≤ 2. We show: Theorem 3.3. Among groups of cardinality γ, the group ⊕γQ serves as a “test space” for the availability of a pseudocompact group topology in this sense: If m(α) ≤ γ ≤ 2 then ⊕γQ admits a (necessarily connect...

Symmetric Transversal Designs with Group Size 3

Compact Group Topologies for R

There is a compact solenoidal group S that is group isomorphic to the additive real numbers R. The existence of 5 leads to a study of compact real groups; that is, compact groups which are group isomorphic to R. The compact real groups are characterized as products of 5. Various conditions on a topological group G are given which are equivalent to G being compact real. It is shown that any comp...

Monoid Kernels and Profinite Topologies on the Free Abelian Group

To each pseudovariety of abelian groups residually containing the integers, there is naturally associated a proonite topology on any nite rank free abelian group. We show in this paper that if the pseudovariety in question has a decidable membership problem, then one can eeectively compute membership in the closure of a subgroup and more generally, in the closure of a rational subset of such a ...