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- Title
Maximal deviation of large powers in the Nottingham group.
- Authors
Aslan, Tuǧba; Hegedüs, Pál
- Abstract
The group of formal power series under substitution over 𝔽p, the so-called Nottingham group, is a pro-p group so it is a metric space. The intertwining of these two structures is an important object of study. This paper is concerned with how the power map influences the distance of elements. Suppose that d(ƒ, g) = d1 while d(ƒ, 1) = d2 ≥ d1. In this paper we provide a sharp bound for d(ƒj, gj) in terms of d1, d2 and the exponent j. This bound confirms a conjecture by K. Keating.
- Subjects
LOGICAL prediction; INTEGERS; ENGEL curve; LINEAR algebra; COMMUTATORS (Operator theory)
- Publication
Journal of Group Theory, 2019, Vol 22, Issue 3, p397
- ISSN
1433-5883
- Publication type
Article
- DOI
10.1515/jgth-2018-0133