Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-28T18:25:44.995Z Has data issue: false hasContentIssue false

Recognising ${\mathbb Z}_p[[t]]$-analytic pro-$p$ groups

Published online by Cambridge University Press:  26 April 2006

RACHEL CAMINA
Affiliation:
Fitzwilliam College, Cambridge, CB3 0DG. e-mail: rdc26@dpmms.cam.ac.uk
MARCUS DU SAUTOY
Affiliation:
Mathematical Institute, 24–29, St. Giles, Oxford, OX1 3LB. e-mail: dusautoy@maths.ox.ac.uk

Abstract

We define a group theoretic criterion on a pro-$p$ group that guarantees the existence of an analytic structure over ${\mathbb Z}_p[[t]]$. This is a one-way analogue of Lazard's succesful answer to the $p$-adic version of Hilbert's Fifth Problem. In the course of the proof we define a $T$-map, a $T$-uniform group and set up a category equivalence between $T$-uniform pro-$p$ groups and powerful ${\mathbb Z}_p[[t]]$-Lie algebras.

Type
Research Article
Copyright
2006 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)