Kazhdan Constants for Sln(Z)
نویسنده
چکیده
In this article we improve the known Kazhdan constant for SLn(Z) with respect to the generating set of the elementary matrices. We prove that the Kazhdan constant is bounded from below by [42 √ n + 860], which gives the exact asymptotic behavior of the Kazhdan constant, as n goes to infinity, since √ 2/n is an upper bound. We can use this bound to improve the bounds for the spectral gap of the Cayley graph of SLn(Fp) and for the working time of the product replacement algorithm for abelian groups.
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عنوان ژورنال:
- IJAC
دوره 15 شماره
صفحات -
تاریخ انتشار 2005