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Title:
Zero-Free Sets in Abelian Groups
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Uncontrolled Keywords:
Sum-free set ; Characteristic function ; Group ; Progression ; Coset.
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Abstract:
The subset A of the group G is called zero-free if the equation x+y+z=0 has no solutions in the set A: The upper and lower estimates were obtained for the maximum cardinality of the zero-free set in an Abelian group, and the asymptotic behavior of the logarithm of the number of zero-free sets in an Abelian group was established. Keywords: Sum-free set, Characteristic function, Group, Progression, Coset.