In 2001 Gowers gave a new proof of Szemeredi's theorem (which asserts that every subset of the integers of positive upper Banach density contains an arithmetic progression of arbitrary finite length). In his proof he has also introduced norms (Gowers norms) on functions on finite groups. In 2005, Host and Kra came up with an infinite, ergodic-theoretical, version of the Gowers norms, called the Gowers-Host-Kra seminorms, and characterized the functions for which the seminorm assigns a value greater than zero. Inspired by this work, Green and Tao (2006) formulated a conjecture (which they proved in a joint work with Ziegler in 2012) about the structure of functions with positive Gowers norms from which they deduced the existence of prime solutions to certain families of linear equations. It was then widely believed that there is a correspondence between the finitary Gowers norms and the infinitary Gowers-Host-Kra seminorms. In this talk we will discuss a recent result by Jamneshan and Tao who have find such a correspondence between the Gowers norms of arbitrary finite abelian groups G, and the Gowers-Host-Kra seminorms associated with ergodic actions of the countable infinite-rank non-torsion abelian group.