$G{L}_n({\mathbb{F}}_q)$-analogues of some properties of $n$-cycles in ${\mathfrak{S}}_n$

We give analogues in the finite general linear group of two elementary results concerning long cycles and transpositions in the symmetric group: first, that the long cycles are precisely the elements whose minimum-length factorizations into transpositions yield a generating set, and second, that a long cycle together with an appropriate transposition generates the whole symmetric group.