Title: Degree of commutativity on general lamplighter groups

Abstract: 

Based on joint work with de las Heras and Klopsch, I will discuss results and open questions regarding the degree of commutativity in finitely generated (infinite) groups of lamplighter type, namely wreath products where the top group is infinite cyclic. 

Firstly, I will focus on the foundational work of Antolín, Martino and Ventura. I aim to explain the main conjecture of whether any group of exponential group growth has degree of commutativity equal to zero, and provide results in its favor. Finally, I will show the new evidence we produced: the conjecture holds in the setting of general lamplighter groups.