The Erdős-Heilbronn problem for finite groups

Paul Balister; Jeffrey Paul Wheeler

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An abstract and generalized approach to the Vitali theorem on nonmeasurable sets

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Here we present abstract formulations of two theorems of Solecki which deal with some generalizations of the classical Vitali theorem on nonmeasurable sets in spaces with transformation groups.

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Let G be an additive finite abelian group, and let S be a sequence over G. We say that S is regular if for every proper subgroup H ⊆ G, S contains at most |H|-1 terms from H. Let ₀(G) be the smallest integer t such that every regular sequence S over G of length |S| ≥ t forms an additive basis of G, i.e., every element of G can be expressed as the sum over a nonempty subsequence of S. The constant ₀(G) has been determined previously only for the elementary abelian groups. In this paper,...