An addition theorem for Abelian groups of order pq
โ Scribed by George T. Diderrich
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 597 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let \(a_{1}, \ldots, a_{k}\) be a sequence of elements in an Abelian group of order \(n\) (repetition allowed). In this paper, we give two sufficient conditions such that an element \(g \in G\) can be written in the form \(g=a_{i_{1}}+a_{i_{2}}+\cdots+a_{i_{n}}, 1 \leqslant i_{1}<i_{2}<\cdots<i_{n}
Let S=(a 1 , a 2 , ..., a 2n&1 ) be a sequence of 2n&1 elements in an Abelian group G of order n (written additively). For a # G, let r(S, a) be the number of subsequences of length exactly n whose sum is a. Erdo s et al. [1] proved that r(S, 0) 1. In [2], Mann proved that if n (=p) is a prime, then
The following result gives a partial answer to a question of R. M. Wilson regarding the existence of group divisible designs of large order. Let k and u be positive integers, 2 [ k [ u. Then there exists an integer m 0 =m 0 (k, u) such that there exists a group divisible design of group type m u wit
when A is a torsion-free abelian group of rank one. As a consequence he was able to show that a finite rank torsion-free group M satisfies M ( nat M\*\* if and only if M F A I and pM s M precisely when pA s A, where ลฝ . M\*sHom y, A . Using this Warfield obtained a characterization of Z ลฝ . w x the