Tarski numbers of groups
Seminar
Speaker
Gili Golan (Bar-Ilan University)
Date
26/03/2014 - 10:30Add to Calendar
2014-03-26 10:30:00
2014-03-26 10:30:00
Tarski numbers of groups
The Tarski number of a group G is the minimal number of pieces in a paradoxical decomposition of it. We investigate how Tarski numbers may change under various group-theoretic operations. Using these estimates and known properties of Golod-Shafarevich groups, we show that the there are 2-generated groups with property (T) and arbitrarily large Tarski numbers.
We also prove that there exist groups with Tarski number 6. These provide the first examples of non-amenable groups without free subgroups whose Tarski number has been computed precisely.
Joint work with Mikhail Ershov and Mark Sapir.
http://arxiv.org/abs/1401.2202
אוניברסיטת בר-אילן - Department of Mathematics
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
Abstract
The Tarski number of a group G is the minimal number of pieces in a paradoxical decomposition of it. We investigate how Tarski numbers may change under various group-theoretic operations. Using these estimates and known properties of Golod-Shafarevich groups, we show that the there are 2-generated groups with property (T) and arbitrarily large Tarski numbers.
We also prove that there exist groups with Tarski number 6. These provide the first examples of non-amenable groups without free subgroups whose Tarski number has been computed precisely.
Joint work with Mikhail Ershov and Mark Sapir.
Last Updated Date : 20/03/2014
