The theory of generalized Hall
planes of odd or zero characteristic has been developed by P. B. Kirkpatrick who has
obtained a characterization of the odd order Hall planes, within the class of odd
order generalized Hall planes, in terms of their homologies with affine axis.
N. L. Johnson has pointed out that odd order generalized Hall planes are derivable
and has characterized them in terms of their derived planes. In this paper the results
of Kirkpatrick are established in the case of generalised Hall planes of characteristic
two and the results of Johnson in the case of generalized Hall planes of even order.
Also, a characterization of the even order Hall planes, within the class of even
order generalized Hall planes, in terms of their elations with affine axis, is
obtained.
