Normal Subgroups in Substitution Groups of Formal Power Series

✍ Scribed by Benjamin Klopsch

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 128 KB
• Volume: 228
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.8219

✦ Synopsis

Let R be a commutative ring with 1, and let R = t + t 2 R͠t͡ be the group of normalized formal power series over R under substitution. In this paper we investigate the connection between the ideal structure of R and the normal subgroup structure of R . In particular, we show that, if K is a finite field of characteristic not equal to two, then every proper quotient group of the so-called Nottingham group K is finite. As a further application we consider the profinite completion of the group R . We show that, if every additive subgroup of finite index in R contains an ideal of finite index in R, then R ∼ = R .