Difference bases in finite Abelian groups
نویسندگان
چکیده
منابع مشابه
Additive Bases in Abelian Groups
Let G be a finite, non-trivial abelian group of exponent m, and suppose that B1, . . . , Bk are generating subsets of G. We prove that if k > 2m ln log2 |G|, then the multiset union B1 ∪ · · · ∪ Bk forms an additive basis of G; that is, for every g ∈ G there exist A1 ⊆ B1, . . . , Ak ⊆ Bk such that g = ∑k i=1 ∑ a∈Ai a. This generalizes a result of Alon, Linial, and Meshulam on the additive base...
متن کاملDesigning Local Orthogonal Bases on Finite Groups I: Abelian Case
(a) (b) (c) b b ˆ Figure 1: Geometric interpretation of the orthogonalization procedure using the Fourier transform as a tool. The group is ? = fI; V g, where V performs the exchange of the components of vectors from R 2. (a) Projection of b on the ?-invariant subspaces relative to U 1 and U ?1. (b) Normalization of the two projections. (c) Recombination of the normalized projections yielding t...
متن کاملDifference Bases in Dihedral Groups
A subset B of a group G is called a difference basis of G if each element g ∈ G can be written as the difference g = ab−1 of some elements a, b ∈ B. The smallest cardinality |B| of a difference basis B ⊂ G is called the difference size of G and is denoted by ∆[G]. The fraction ð[G] := ∆[G]/ √ |G| is called the difference characteristic of G. We prove that for every n ∈ N the dihedral group D2n ...
متن کاملDecomposing finite Abelian groups
This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann Hypothesis) also leads to an efficient algorithm for computing class numbers (known to be at least as difficult as factoring).
متن کاملFactoring finite abelian groups
It is shown that if in the factorization of a finite cyclic group each factor has either prime power order or order equal to the product of two primes then one factor must be periodic. This is shown to be the best possible result of this type. 2004 Elsevier Inc. All rights reserved.
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: Acta Scientiarum Mathematicarum
سال: 2019
ISSN: 0001-6969
DOI: 10.14232/actasm-017-586-x