Abstract. We prove that every infinite, discrete abelian group admits a pair of $I_{0}$ sets whose union is not $I_{0}$. In particular, this implies that every such group contains a Sidon set that is not $I_{0}$.
DOI: 10.14232/actasm-016-518-4
AMS Subject Classification
(1991): 43A46
Keyword(s):
Sidon set,
$I_{0}$ set,
Kronecker set
Received March 24, 2016, and in revised form August 5, 2016. (Registered under 18/2016.)
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