DTC ultrafilters on groups
Group Theory
2021-04-15 v3 General Topology
Abstract
We say that an ultrafilter on an infinite group is DTC if it determines the topological centre of the semigroup . We prove that DTC ultrafilters do not exist for virtually BFC groups, and do exist for the countable groups that are not virtually FC. In particular, an infinite finitely generated group is virtually abelian if and only if it does not admit a DTC ultrafilter.
Keywords
Cite
@article{arxiv.1910.07505,
title = {DTC ultrafilters on groups},
author = {Jan Pachl and Juris Steprāns},
journal= {arXiv preprint arXiv:1910.07505},
year = {2021}
}
Comments
8 pages. Version 2 includes changes in section 3 and a correction in Example 5.4. Version 3 incorporates minor editing changes