Abstract
Let G be a finite abelian group (written additively) of rank r with invariants n 1, n 2, . . . , n r , where n r is the exponent of G. In this paper, we prove an upper bound for the Davenport constant D(G) of G as follows; D(G) ≤ n r + n r-1 + (c(3) − 1)n r-2 + (c(4) − 1) n r-3 + · · · + (c(r) − 1)n 1 + 1, where c(i) is the Alon–Dubiner constant, which depends only on the rank of the group \({{\mathbb Z}_{n_r}^i}\). Also, we shall give an application of Davenport’s constant to smooth numbers related to the Quadratic sieve.
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Chintamani, M.N., Moriya, B.K., Gao, W.D. et al. New upper bounds for the Davenport and for the Erdős–Ginzburg–Ziv constants. Arch. Math. 98, 133–142 (2012). https://doi.org/10.1007/s00013-011-0345-z
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DOI: https://doi.org/10.1007/s00013-011-0345-z