Recent progress in Subset Combinatorics of Groups

Abstract

We systematize and analyze some results obtained in Subset Combinatorics of G groups after publications the previous surveys [1–4]. The main topics: the dynamical and descriptive characterizations of subsets of a group relatively their combinatorial size, Ramsey-product subsets in connection with some general concept of recurrence in G-spaces, new ideals in the Boolean algebra PG of all subsets of a group G and in the Stone-Cech compactification βG of G, the combinatorial derivation.