## Innovations in Incidence Geometry

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

#### Abstract

In this paper, it is shown that any projective plane $Π$ of order $n ≤ q 4$, $q$ 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 $n ≤ q 3$, actually, $n = q$, $q 2$ or $q 3$.

#### Article information

Source
Innov. Incidence Geom., Volume 6-7, Number 1 (2007), 73-94.

Dates
First available in Project Euclid: 28 February 2019

https://projecteuclid.org/euclid.iig/1551323171

Digital Object Identifier
doi:10.2140/iig.2008.6.73

Mathematical Reviews number (MathSciNet)
MR2515259

Zentralblatt MATH identifier
1172.51005

#### Citation

Biliotti, Mauro; Montinaro, Alessandro. On the finite projective planes of order up to $q^4$, $q$ odd, admitting $\mathsf{PSL}(3,q)$ as a collineation group. Innov. Incidence Geom. 6-7 (2007), no. 1, 73--94. doi:10.2140/iig.2008.6.73. https://projecteuclid.org/euclid.iig/1551323171