# Element structure of general semilinear group of degree two over a finite field

This article describes the element structure of the general semilinear group of degree two over a finite field of size $q = p^r$, where $p$ is the characteristic of the field. The Galois group of the extension $\mathbb{F}_q/\mathbb{F}_p$ is a cyclic group of order $r$, generated by the $p$-power map (the Frobenius automorphism). Note that $r = \log_p q$
order of the group $r(q^2 - 1)(q^2 - q)$