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DTC ultrafilters on groups

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Abstract

We say that an ultrafilter on an infinite group G is DTC if it determines the topological centre of the semigroup \(\beta G\). If G has a subgroup of finite index in which conjugacy classes are all finite and uniformly bounded in size, then G does not admit a DTC ultrafilter. On the other hand, if G has no subgroup of finite index in which all conjugacy classes are finite, then G does admit a DTC ultrafilter. It follows that an infinite finitely generated group admits a DTC ultrafilter if and only if it has no abelian subgroup of finite index.

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Acknowledgements

We wish to thank the anonymous referee for a number of valuable comments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, Toronto, ON, Canada

    Jan Pachl & Juris Steprāns

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  1. Jan Pachl
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  2. Juris Steprāns
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Correspondence to Jan Pachl.

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Communicated by Anthony To-Ming Lau.

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The research of Juris Steprāns is supported by NSERC.

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Pachl, J., Steprāns, J. DTC ultrafilters on groups. Semigroup Forum 102, 517–527 (2021). https://doi.org/10.1007/s00233-020-10132-3

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  • DOI: https://doi.org/10.1007/s00233-020-10132-3

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