## Algebra & Number Theory

### Weakly commensurable $S$-arithmetic subgroups in almost simple algebraic groups of types $\mathsf{B}$ and $\mathsf{C}$

#### Abstract

Let $G1$ and $G2$ be absolutely almost simple algebraic groups of types $Bℓ$ and $Cℓ$, respectively, defined over a number field $K$. We determine when $G1$ and $G2$ have the same isomorphism or isogeny classes of maximal $K$-tori. This leads to the necessary and sufficient conditions for two Zariski-dense $S$-arithmetic subgroups of $G1$ and $G2$ to be weakly commensurable.

#### Article information

Source
Algebra Number Theory, Volume 7, Number 5 (2013), 1147-1178.

Dates
Revised: 29 April 2012
Accepted: 7 June 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513730008

Digital Object Identifier
doi:10.2140/ant.2013.7.1147

Mathematical Reviews number (MathSciNet)
MR3101075

Zentralblatt MATH identifier
1285.20045

#### Citation

Garibaldi, Skip; Rapinchuk, Andrei. Weakly commensurable $S$-arithmetic subgroups in almost simple algebraic groups of types $\mathsf{B}$ and $\mathsf{C}$. Algebra Number Theory 7 (2013), no. 5, 1147--1178. doi:10.2140/ant.2013.7.1147. https://projecteuclid.org/euclid.ant/1513730008

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