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A reduction theorem on purely singular splittings of cyclic groups

1995
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Proceedings of the American Mathematical Society
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A set M of nonzero integers is said to split a finite abelian group G if there is a subset S of G for which M • S = G\{0] . If, moreover, each prime divisor of |G| divides an element of M, we call the splitting purely singular. It is conjectured that the only finite abelian groups which can be split by {1, ... , k} in a purely singular manner are the cyclic groups of order 1, k + 1 and 2k + 1 . We show that a proof of this conjecture can be reduced to a verification of the case gcd(|G|, 6) = 1 .

doi:10.1090/s0002-9939-1995-1277139-2
fatcat:4h3cypx6a5ajthg2x4avuohrgq