, Volume 91, Issue 1-3, pp 349-371

The order of a typical matrix with entries in a finite field

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Abstract

IfA is an invertiblen×n matrix with entries in the finite field Fq, letT n (A) be its minimum period or exponent, i.e. its order as an element of the general linear group GL(n,q). The main result is, roughly, that \(T_n (A) = q^{n - } (log n)^{2 + 0(1)} \) for almost everyA.

Supported by N.S.F. (D.M.S. 9101753).