Element structure of special affine group of degree two over a finite field

This article describes the element structure of $$SA(2,q)$$, the special affine group of degree two over a finite field of size $$q$$, where $$q$$ is a prime power. We denote by $$p$$ the characteristic of the field, so $$p$$ is a prime number. Thus, $$q = p^r$$ for some positive integer $$r$$.