Type: Article

On p-compact topologies on certain Abelian groups

García-Ferreira, S., Tomita, A. H., Trianon-Fraga, J.;

Abstract:

Given a selective ultrafilter p is an element of w & lowast;, we prove that there exists a p-compact group topology on Q((c)) without nontrivial convergent sequences and a closed subgroup H subset of Q((c))which contains an element not divisible by any n is an element of omega (Q((c))does not admit a p-compact topology for any p is an element of omega & lowast;. Given H a group and G a subgroup of Q which is not n-divisible, for some prime number n > 1, but is m-divisible for each prime number m not equal n, we show that a group topology compatible with H (c) G cannot be p-compact for any p is an element of omega & lowast