Functorial topologies and finite-index subgroups of abelian groups

Details Functorial topologies and finite-index subgroups of abelian groups Functorial topologies and finite-index subgroups of abelian groups

2011-03-23

arxiv.org/abs/1103.4565v1

Mathematics

General Topology

19 pages

Scientific paper

In the general context of functorial topologies, we prove that in the lattice of all group topologies on an abelian group, the infimum between the Bohr topology and the natural topology is the profinite topology. The profinite topology and its connection to other functorial topologies is the main objective of the paper. We are particularly interested in the poset C(G) of all finite-index subgroups of an abelian group G, since it is a local base for the profinite topology of G. We describe various features of the poset C(G) (its cardinality, its cofinality, etc.) and we characterize the abelian groups G for which C(G)\{G} is cofinal in the poset of all subgroups of G ordered by inclusion. Finally, for pairs of functorial topologies T, S we define the equalizer E(T,S), which permits to describe relevant classes of abelian groups in terms of functorial topologies.

Affiliated with

Also associated with

No associations

Rating

Functorial topologies and finite-index subgroups of abelian groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Functorial topologies and finite-index subgroups of abelian groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Functorial topologies and finite-index subgroups of abelian groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-441572