Algebra & Number Theory

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

Michael Larsen

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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).

Article information

Source
Algebra Number Theory, Volume 4, Number 8 (2010), 1029-1038.

Dates
Received: 15 May 2009
Revised: 21 July 2010
Accepted: 21 July 2010
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729607

Digital Object Identifier
doi:10.2140/ant.2010.4.1029

Mathematical Reviews number (MathSciNet)
MR2832632

Zentralblatt MATH identifier
1219.22011

Subjects
Primary: 20G25: Linear algebraic groups over local fields and their integers
Secondary: 20G40: Linear algebraic groups over finite fields

Keywords
exponentially generated Nori's theorem $p$-adic Lie group

Citation

Larsen, Michael. Exponential generation and largeness for compact $p$-adic Lie groups. Algebra Number Theory 4 (2010), no. 8, 1029--1038. doi:10.2140/ant.2010.4.1029. https://projecteuclid.org/euclid.ant/1513729607


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