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...
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We study the problem of removing an element from an additive basis in a general abelian group. We introduce analogues of the classical functions X,S and E (defined in the case of N) and obtain bounds on them. Our estimates on the functions SG and EG are valid for general abelian groups G while in the case of XG we show that distinct types of behaviours may occur depending on G.
متن کاملBasic Theory of Additive Abelian Groups
In this chapter we discuss cyclic groups, the quotient group construction, the direct sum construction and the first isomorphism theorem, in the context of additive abelian groups; we also discuss free modules. These concepts are necessary, as well as the matrix theory of Chapter 1, for the study of finitely generated abelian groups in Chapter 3. At the same time the material provides the reade...
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Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables.
متن کاملAbelian Groups, Gauss Periods, and Normal Bases
A result on finite abelian groups is first proved and then used to solve problems in finite fields. Particularly, all finite fields that have normal bases generated by general Gauss periods are characterized and it is shown how to find normal bases of low complexity. Dedicated to Professor Chao Ko on his 90th birthday.
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2010
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042110003216