Algebra & Number Theory
- Algebra Number Theory
- Volume 4, Number 8 (2010), 1029-1038.
Exponential generation and largeness for compact $p$-adic Lie groups
Given a fixed integer , we consider closed subgroups of , where is sufficiently large in terms of . Assuming that the identity component of the Zariski closure of in does not admit any nontrivial torus as quotient group, we give a condition on the () reduction of which guarantees that is of bounded index in .
Algebra Number Theory, Volume 4, Number 8 (2010), 1029-1038.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20G25: Linear algebraic groups over local fields and their integers
Secondary: 20G40: Linear algebraic groups over finite fields
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