Addition Theorems and Group Rings

✍ Scribed by W.D. Gao

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 375 KB
• Volume: 77
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.1996.2731

✦ Synopsis

We establish several addition theorems on finite abelian groups by employing a group ring as a useful tool. Among several results the following is proved. Let p be a prime, and let G=Z p e 1 } } } Z p e n with 1 e 1 } } } e n . Put w=(1Â( p en &1)) _ n i=1 ( p e i &1). Then, for any t ( p en &1) log w+ p e n &2 linear bases B 1 , ..., B t of G their union (with repetitions) t i=1 B i forms an additive basis of G.

1997 Academic

Press

Theorem 1.1. Let G=Z p e 1 } } } Z p e n with 1 e 1 } } } e n , and let w=(1Â( p e n &1)) n i=1 ( p e i &1). Then, f (G) ( p e n &1) log w+ p e n &2.