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Journal of the London Mathematical Society 2000 62(1):27-40; doi:10.1112/S0024610700008863
© 2000 by London Mathematical Society
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© The London Mathematical Society

Restricted Set Addition in Groups I: The Classical Setting

Vsevolod F. Lev

Department of Mathematics, University of Georgia Athens, GA 30602, USA, seva{at}math.uga.edu

Received 25 September 1998. Revision received 10 January 2000.

The existing results are surveyed and several new results are proved for the cardinality of the restricted doubling 2^A = {a' + a'':a',a'' isin A,a' != a''}, where A {subseteq} 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.


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