On derivable Baer-elation planes

Abstract

In [5], Jha and Johnson introduce Baer-elation planes. These are finite translation planes of order $q²$, $q=p^r$ which admit both Baer p-collineation groups and elation groups which normalize each other.By a result of Foulser [3], $p=2$.Jha-Johnson consider, in particular, Baer-elation planes of order $q²$ with kernel $GF(q)$ of type (2,q) or type (q,2). That is, there is a Baer or elation group of order q.By the incompatibility results of Jha-Johnson [7], [8], the corresponding or Baer group has order $≤ 2$.