Restricted sumsets in a finite abelian group
نویسندگان
چکیده
منابع مشابه
On two questions about restricted sumsets in finite abelian groups
Let G be an abelian group of finite order n, and let h be a positive integer. A subset A of G is called weakly h-incomplete if not every element of G can be written as the sum of h distinct elements of A; in particular, if A does not contain h distinct elements that add to zero, then A is called weakly h-zero-sum-free. We investigate the maximum size of weakly hincomplete and weakly h-zero-sum-...
متن کاملOn Restricted Sumsets in Abelian Groups of Odd Order
Let G be an abelian group of odd order, and let A be a subset of G. For any integer h such that 2 ≤ h ≤ |A| − 2, we prove that |h∧A| ≥ |A| and equality holds if and only if A is a coset of some subgroup of G, where h∧A is the set of all sums of h distinct elements of A.
متن کاملRestricted Sumsets in Finite Vector Spaces : the Case
We determine the sharp lower bound for the cardinality of the restricted sumset A+′B = {a + b | a ∈ A, b ∈ B, a 6= b}, where A,B run over all subsets of size r = s = 1 + 3 in a vector space over F3. This solves a conjecture stated in an earlier paper of ours on sumsets and restricted sumsets in finite vector spaces. The analogous problem for an arbitrary prime p remains open. However, we do pro...
متن کاملOn Various Restricted Sumsets
For finite subsets A1, . . . , An of a field, their sumset is given by {a1+ · · ·+an : a1 ∈ A1, . . . , an ∈ An}. In this paper we study various restricted sumsets of A1, . . . , An with restrictions of the following forms: ai − aj 6∈ Sij , or αiai 6= αjaj , or ai + bi 6≡ aj + bj (mod mij). Furthermore, we gain an insight into relations among recent results on this area obtained in quite differ...
متن کاملHow Abelian is a Finite Group?
A well known theorem of G. A. Miller [4] (see also [2]) shows that a p-group of order p" where n > v(v 1)/2 contains an Abelian subgroup of order p° . It is clear that this theorem together with Sylow's Theorem implies that any finite group of large order contains an Abelian p-group of large order . In this note we use simple number theoretic considerations to make this implication more precise...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.06.028