Israel Journal of Mathematics

, Volume 91, Issue 1, pp 349–371

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

  • Eric Schmutz

DOI: 10.1007/BF02761656

Cite this article as:
Schmutz, E. Israel J. Math. (1995) 91: 349. doi:10.1007/BF02761656


IfA is an invertiblen×n matrix with entries in the finite field Fq, letTn(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.

Copyright information

© The Magnes Press 1995

Authors and Affiliations

  • Eric Schmutz
    • 1
  1. 1.Mathematics and Computer Science DepartmentDrexel UniversityPhiladelphiaUSA