Subregular planes admitting elations

Abstract

New classes of subregular planes are constructed that admit elation groups or Baer groups of order >2. Further, we construct a variety of large dimension translation planes admitting many elations.

Lifting Subregular Spreads

“…Hence, by lifting, we may construct an infinite class of translation planes admitting groups of order 8(8 s +1), where s is any odd integer. Indeed, Jha and Johnson [15] have constructed this infinite class directly without lifting.…”

“…In Jha and Johnson [15], it is shown that there is a class of Foulser planes of even order q 2 obtained by the replacement of a set S √ q of √ q mutually disjoint reguli in an orbit under an elation group E of the same order. Furthermore, the axis of E is a line of a regulus R q that intersects each of the reguli of S √ q in a unique component.…”

“…This is a subclass of the class related to inversion-fixed planes. It is shown in [15] that it is possible to 'move' the set S √ q so as to obtain a set of reguli in an orbit under E but where the reguli are disjoint from R q . In this case, it is possible to also derive R q to obtain a subregular plane of order q 2 admitting a Baer group of order √ q.…”