Vol. 6, No. 1, 2008

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On the finite projective planes of order up to $q^4$, $q$ odd, admitting $\mathsf{PSL}(3,q)$ as a collineation group

Mauro Biliotti and Alessandro Montinaro

Vol. 6 (2008), No. 1, 73–94
Abstract

In this paper, it is shown that any projective plane Π of order n q4, q odd, that admits a group GPSL(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 q3, actually, n = q, q2 or q3.

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