On central collineations of derived semifield planes

LetG denote the collineation group generated by the set of all affine central collineations in a derived semifield plane. We present a characterization of the Hall planes in terms of the order ofG. This essentially allows the extension of the theorems of Kirkpatrick and Rahilly on generalized Hall planes to arbitrary derived semifield planes. That is, a derived semifield plane of order q² is a Hall plane precisely when it admits q+1 involutory central collineations.