Thetranslation planes of order 81 admitting

Abstract

Johnson and Prince have classified all translation planes of order 81 that admit , where the 3-elements are elations. In this article, it is shown that whenever acts as a collineation group on a translation plane of order 81, the problem can always be reduced to the elation case. Hence, there is a complete classification of all translation planes of order 81 admitting ; there are exactly 14 translation planes of order 81 admitting .