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arxiv: 1205.1458 · v1 · pith:72ZPNG3Tnew · submitted 2012-05-07 · 🧮 math.GR · math.NT

Weakly commensurable S-arithmetic subgroups in almost simple algebraic groups of types B and C

classification 🧮 math.GR math.NT
keywords algebraicalmostcommensurablegroupss-arithmeticsimplesubgroupstypes
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Let G and G' be absolutely almost simple algebraic groups of types B and C respectively, of rank at least 3, and defined over a number field K. We determine when G and G' 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 G and G' to be weakly commensurable.

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