Orthogonal starters in finite abelian groups
β Scribed by J.D. Horton
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 868 KB
- Volume
- 79
- Category
- Article
- ISSN
- 0012-365X
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π 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}
## Abstract We find all possible lengths of circuits in Cayley digraphs of twoβgenerated abelian groups over the twoβelement generating sets and over certain threeβelement generating sets.
In this paper the following theorem is proved. Let G be a finite Abelian group of order n. Then, n+D(G )&1 is the least integer m with the property that for any sequence of m elements a 1 , ..., a m in G, 0 can be written in the form 0= a 1 + } } } +a in with 1 i 1 < } } } <i n m, where D(G) is the