Student Number Theory seminar

Speaker

Cassie Naymie, Department of Pure Mathematics, University of Waterloo

3-APs in finite abelian groups: abstract

We say that {x, y, z} forms a three term arithmetic progression (or 3-AP) if z = 2y - x. For a finite abelian group G we’re interested in finding the largest cardinality of all subsets A ⊂ G with A containing no 3-APs. We denote this cardinality by D(G). In this talk we will present a result of Roy Meshulam’s proving the following: If G is a finite abelian group of odd order, then D(G) = D(\mathbb{Z}_{k_1}\oplus\mathbb{Z}_{k_2}\oplus · · ·\oplus\mathbb{Z}_{k_n}) ≤ 2(k_1k_2 · · · k_n)/n = 2|G|/n (here n is the number of components in G).