Vol. 4, No. 8, 2010

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Exponential generation and largeness for compact $p$-adic Lie groups

Michael Larsen

Vol. 4 (2010), No. 8, 1029–1038
Abstract

Given a fixed integer n, we consider closed subgroups G of GLn(p), where p is sufficiently large in terms of n. Assuming that the identity component of the Zariski closure G of G in GLn,p does not admit any nontrivial torus as quotient group, we give a condition on the ( modp) reduction of G which guarantees that G is of bounded index in GLn(p) G(p).

Keywords
exponentially generated, Nori's theorem, $p$-adic Lie group
Mathematical Subject Classification 2000
Primary: 20G25
Secondary: 20G40
Milestones
Received: 15 May 2009
Revised: 21 July 2010
Accepted: 21 July 2010
Published: 24 February 2011
Authors
Michael Larsen
Department of Mathematics
Rawles Hall
Indiana University
Bloomington, IN 47405-5701
United States
http://mlarsen.math.indiana.edu/~larsen/