ON KAZHDAN CONSTANTS OF FINITE INDEX SUBGROUPS IN SLn(ℤ)
| Autor: | Uzy Hadad |
|---|---|
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | International Journal of Algebra and Computation. 22:1250026 |
| ISSN: | 1793-6500 0218-1967 |
| DOI: | 10.1142/s0218196712500269 |
| Popis: | We prove that for any finite index subgroup Γ in SL n(ℤ), there exists k = k(n) ∈ ℕ, ϵ = ϵ(Γ) > 0, and an infinite family of finite index subgroups in Γ with a Kazhdan constant greater than ϵ with respect to a generating set of order k. On the other hand, we prove that for any finite index subgroup Γ of SL n(ℤ), and for any ϵ > 0 and k ∈ ℕ, there exists a finite index subgroup Γ′ ≤ Γ such that the Kazhdan constant of any finite index subgroup in Γ′ is less than ϵ, with respect to any generating set of order k. In addition, we prove that the Kazhdan constant of the principal congruence subgroup Γn(m), with respect to a generating set consisting of elementary matrices (and their conjugates), is greater than [Formula: see text], where c > 0 depends only on n. For a fixed n, this bound is asymptotically best possible. |
| Databáze: | OpenAIRE |
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