A reduction theorem on purely singular splittings of cyclic groups
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- by Andrew J. Woldar PDF
- Proc. Amer. Math. Soc. 123 (1995), 2955-2959 Request permission
Abstract:
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 $M \cdot S = G\backslash \{ 0\}$. 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 $\{ 1, \ldots ,k\}$ 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 $\gcd (|G|,6) = 1$.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2955-2959
- MSC: Primary 20K01; Secondary 20D60
- DOI: https://doi.org/10.1090/S0002-9939-1995-1277139-2
- MathSciNet review: 1277139