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RESTRICTED SET ADDITION IN GROUPS I: THE CLASSICAL SETTING

Published online by Cambridge University Press:  30 October 2000

VSEVOLOD F. LEV
VSEVOLOD F. LEV
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA; seva@math.uga.edu
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Abstract

The existing results are surveyed and several new results are proved for the cardinality of the restricted doubling 2ˆA = {a′ + a″:a′,a″ ∈ A,a′ ≠ a″}, where A ⊆ 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.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 62 , Issue 1 , August 2000 , pp. 27 - 40
Copyright
The London Mathematical Society 2000

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