Semifield planes of odd order that admit a subgroup of autotopisms isomorphic to A 4

Abstract

We develop an approach to constructing and classification of semifield projective planes with the use of a linear space and a spread set. We construct a matrix representation of the spread set of a semifield plane of odd order that admits a Baer involution in the translation complement or a subgroup of autotopisms isomorphic to the alternating group A4. We give examples of semifield planes of order 81 satisfying the above indicated condition.