On the finite projective planes of order up to q4, q odd, admitting PSL(3,q) as a collineation group

In this paper, it is shown that any projective plane $Π$ of order $n \leq q^{4}$ , $q$ odd, that admits a group $G ≅ PSL (3, q)$ as a collineation group contains a $G$ -invariant Desarguesian subplane of order $q$ . Moreover, the involutions and suitable $p$ -elements in $G$ are homologies and elations of $Π$ , respectively. In particular, if $n \leq q^{3}$ , actually, $n = q$ , $q^{2}$ or $q^{3}$ .

Keywords

projective plane, collineation group, orbit

Mathematical Subject Classification 2000

Primary: 20B25, 51E15

Milestones

Received: 10 December 2007

Authors

Mauro Biliotti
Dipartimento di Matematica e Fisica Università del Salento Lecce Italy

Alessandro Montinaro

Vol. 6+7, No. 1, 2008

Mauro Biliotti and Alessandro Montinaro

Abstract

Keywords

Mathematical Subject Classification 2000

Milestones

Authors