Congruence subgroup growth of arithmetic groups in positive characteristic. (English) Zbl 1036.20043

A new uniform bound for subgroup growth of a Chevalley group \(G\) over the local ring \(\mathbb{F}[\![t]\!]\) and also over local pro-\(p\) rings of higher Krull dimension is obtained. This is applied to bound the congruence subgroup growth of arithmetic groups over global fields of positive characteristic. This improves an upper bound obtained by Lubotzky.


20H05 Unimodular groups, congruence subgroups (group-theoretic aspects)
20E07 Subgroup theorems; subgroup growth
20G30 Linear algebraic groups over global fields and their integers
17B45 Lie algebras of linear algebraic groups
20E18 Limits, profinite groups
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