Restricted set addition in groups I: The classical setting

摘要

The existing results are surveyed and several new results are proved for the cardinality of the restricted doubling 2 boolean AND A = {a' + a":a', a" epsilon A, a' not equal a"}, where A subset of or equal to G is a subset of the set of elements of an (additively written) group G. In particular, known estimates for G = Z and G = Z/pZ are improved and a first-of-a-kind general estimate valid for arbitrary G is given. [References: 12]