Speaker: Chimere Anabanti (University of Pretoria, South Africa)
Abstract: A non-empty subset S of a group G is called a product-free set if S and SS have no element in common. Let S be a maximal by inclusion product-free set in a finite group G. We say that S fills G if every non-identity element of G is contained in the union of S and SS. A finite group G is called a filled group if every maximal by inclusion product-free set in G fills G. In this talk, we shall give an application of product-free sets to combinatorics, as well as discuss the known finite filled groups.
Part of this presentation is a joint work with Sarah Hart and Grahame Erskine.