On some pro-p groups from infinite-dimensional Lie theory

2013/02/18 by Inna Capdeboscq, Capdeboscq, Inna, Bertrand Rémy +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1302.4174

16 pages

arxiv created 2013/02/18 · openalex publication_date 2013/02/18 · arxiv updated 2013/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We initiate the study of some pro-p-groups arising from infinite-dimensional Lie theory. These groups are completions of some subgroups of incomplete Kac-Moody groups over finite fields, with respect to various completions of algebraic or geometric origin. We show topological finite generation for the pro-p Sylow subgroups in many complete Kac-Moody groups. This implies abstract simplicity of the latter groups. We also discuss with the question of (non-)linearity of these pro-p groups.

Related

• Pro-Lie groups which are infinite-dimensional Lie groups
• Kac-Moody Groups and Completions
• Pro-Lie Groups: A survey with Open Problems
• Topological simplicity, commensurator super-rigidity and non-linearities of Kac-Moody groups
• Pro-p groups with constant generating number on open subgroups