On weak Sierpi\'nski sets in groups and free subgroups
Group Theory
2019-03-21 v3
Abstract
In this paper we discuss the problem of existence of so called weak Sierpi\'nski sets in groups. It is known that group has a Sierpi\'nski subset if and only if it contains a free subgroup. In their paper, Tomkowicz and Wagon conjectured that an analogous result holds also for the weaker condition. We derive a number of properties of groups with weak Sierpi\'nski subsets and use them to prove the above mentioned conjecture. This is an improved version of arXiv:1805.11486. Some of the included proofs have been simplified and shortened.
Keywords
Cite
@article{arxiv.1805.11486,
title = {On weak Sierpi\'nski sets in groups and free subgroups},
author = {Agnieszka Bier and Piotr Słanina},
journal= {arXiv preprint arXiv:1805.11486},
year = {2019}
}
Comments
The results elaborated in this paper have been improved and complemented in another work arXiv:1903.07043