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.
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