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Abért, Miklós; Nikolov, Nikolay; Szegedy, Balázs

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

Duke Math. J. 117, No. 2, 367-383 (2003).
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.
Reviewer: L. N. Vaserstein (University Park)

Cited in 3 Documents

MSC:

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

Keywords:

congruence subgroup growth; arithmetic groups; analytic groups; numbers of open subgroups
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\textit{M. Abért} et al., Duke Math. J. 117, No. 2, 367--383 (2003; Zbl 1036.20043)
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