The Erdős-Heilbronn problem in Abelian groups
Solving a problem of Erdős and Heilbronn, in 1994 Dias da Silva and Hamidoune proved that ifA is a set ofk residues modulo a primep,p≥2k−3, then the number of different elements of ℤ/pℤ that can be written in the forma+a′ wherea, a′ ∈A,a∈a′, is at least 2k−3. Here we extend this result to arbitrary Abelian groups in which the order of any nonzero element is at least 2k−3.
KeywordsAbelian Group London Mathematical Society Congruence Class Small Positive Integer Prime Power Order
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