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Journal of the London Mathematical Society Advance Access published online on October 4, 2007
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm055
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© 2007 London Mathematical Society

ANALYTIC GROUPS OVER GENERAL PRO-p DOMAINS

Andrei Jaikin-Zapirain and Benjamin Klopsch

Departamento de Matemáticas
Facultad de Ciencias
Universidad Autónoma de Madrid
Canto Blanco Ciudad Universitaria
28049 Madrid
Spain
Mathematisches Institut
Heinrich-Heine-Universität
40225 Düsseldorf
Germany

While the theory of Lie groups is highly developed in characteristic 0, comparatively little is known about analytic groups over local fields of positive characteristic p. More generally, one can consider groups which are analytic over pro-p domains R, without restricting the Krull dimension to 1. Natural examples are rings of the form R = Fp[t1,...,tm].

Experience shows that analytic pro-p groups, also in this general sense, possess interesting properties, and one faces the challenge of developing a systematic structure theory for such objects. With this long-term goal in mind, we collect several fundamental results which provide information about the structure of R-analytic pro-p groups. In particular, we establish a useful criterion for isolating Fp[t]-analytic groups within the class of finitely generated pro-p groups.

Current address: Department of Mathematics Royal Holloway University of London Egham Surrey TW20 0EE United Kingdom benjamin.klopsch{at}rhul.ac.uk

2000 Mathematics Subject Classification 20E18 (primary), 22E20, 20F40, 20G25 (secondary).

The work of the first author was supported by the FEDER and the MEC Grant MTM2004-04665. The results in this paper form part of the second author's habilitation thesis at the University of Düsseldorf.

Received July 13, 2006;
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