Sentence:  The object of this note is to observe that it is possible to calculate the <WSD>order</WSD> of an element A of G = \mathit{GL}(d,q) on average using O(d^3 \mathsf{log}\ q) field operations, assuming that q^i-1 has been factorised for i\le d. 
Meaning of the word marked with <WSD> tags:  For given group "G" and element "g" ∈ "G", the smallest positive natural number "n", if it exists, such that (using multiplicative notation), "gn = e", where "e" is the identity element of "G"; "if no such number exists, the element is said to be of '''infinite order''' (or sometimes '''zero order''')."