## Innovations in Incidence Geometry

### The general structure of the projective planes admitting $\mathrm{PSL}(2,q)$ as a collineation group

Alessandro Montinaro

#### Abstract

Projective planes of order $n$ admitting $PSL(2,q)$, $q>3$, as a collineation group are investigated for $n≤q2$. As a consequence, affine planes of order $n$ admitting $PSL(2,q)$, $q>3$, as a collineation group are classified for $n and $(q,n)≠(5,16)$. Finally, a complete classification of the translation planes order $n$ that admitting $PSL(2,q)$, $q>3$, as a collineation group is obtained for $n≤q2$.

#### Article information

Source
Innov. Incidence Geom., Volume 5, Number 1 (2007), 35-116.

Dates
Accepted: 27 September 2007
First available in Project Euclid: 28 February 2019

https://projecteuclid.org/euclid.iig/1551323210

Digital Object Identifier
doi:10.2140/iig.2007.5.35

Mathematical Reviews number (MathSciNet)
MR2401255

Zentralblatt MATH identifier
1155.51005

#### Citation

Montinaro, Alessandro. The general structure of the projective planes admitting $\mathrm{PSL}(2,q)$ as a collineation group. Innov. Incidence Geom. 5 (2007), no. 1, 35--116. doi:10.2140/iig.2007.5.35. https://projecteuclid.org/euclid.iig/1551323210

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