The order of a typical matrix with entries in a finite field
type: Item
instance of: scholarly article
title: The order of a typical matrix with entries in a finite field
zbMATH Open document ID: 0840.15016
DOI: 10.1007/BF02761656
published in: Israel Journal of Mathematics
publication date: 1996-06-24T00:00:00Z
review text: An estimation for the order or minimum period \(T_n (A)\) of a (typical) matrix \(A \in {\mathcal G}_n\) is given, where \({\mathcal G}_n\) is the group of invertible matrices over a finite field \(\mathbb{F}_q\). It is shown that \(T_n (A) = q^{n - (\log n)^{2 + o(1)}}\) for almost every \(A\). This result is a consequence of a similar theorem which is proved for the order of a monic polynomial and it is obtained by using an approximation theorem of \textit{J. C. Hansen} and the author [Math. Proc. Camb. Philos. Soc. 114, No. 3, 507-515 (1993; Zbl 0793.15013)].
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 11T99
zbMATH DE Number: 820108
zbMATH Keywords: minimum period
zbMATH Keywords: group of invertible matrices over a finite field
zbMATH Keywords: monic polynomial
author: Eric Schmutz
reviewed by: Valeriu Prepeliţă
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 820108