The critical number of finite abelian groups
The critical number of finite abelian groups
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DOI：
10.1016/j.jnt.2009.05.016
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发表时间：
2008-10
影响因子：
0.7
通讯作者：
M. Freeze;Weidong Gao;A. Geroldinger
中科院分区：
文献类型：
--
作者：
M. Freeze;Weidong Gao;A. Geroldinger
设G是一个可加的有限阿贝尔群。G的临界值cr (G)是最小的正整数ℓ这样每个子集S⊂G∖{0}| S |⩾ℓ以下持有:G的每一个元素可以写成一个非空的和不同的元素从美国关键的数量首次研究了p ErdőS和h . 1964年海尔布隆,由于许多作者的贡献和cr (G)的值是已知的所有有限阿贝尔组G除了G≅Z / pqZ p, q是质数,p +⌊2 p−2⌋+ 1 < < 2 p。我们确定cr(G)=p+q−2。
Let G be an additive, finite abelian group. The critical number cr(G) of G is the smallest positive integer ℓ such that for every subset S⊂G∖{0} with |S|⩾ℓ the following holds: Every element of G can be written as a nonempty sum of distinct elements from S. The critical number was first studied by P. Erdős and H. Heilbronn in 1964, and due to the contributions of many authors the value of cr(G) is known for all finite abelian groups G except for G≅Z/pqZ where p,q are primes such that p+⌊2p−2⌋+1<q<2p. We determine that cr(G)=p+q−2 for such groups.