Algebra & Number Theory

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

Skip Garibaldi and Andrei Rapinchuk

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Let G1 and G2 be absolutely almost simple algebraic groups of types B and C, 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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20G15: Linear algebraic groups over arbitrary fields
Secondary: 11E57: Classical groups [See also 14Lxx, 20Gxx] 14L35: Classical groups (geometric aspects) [See also 20Gxx, 51N30] 20G30: Linear algebraic groups over global fields and their integers

isogenous maximal tori weak commensurability isomorphic maximal tori


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.

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