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

Mauro Biliotti and Alessandro Montinaro

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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
Received: 10 December 2007
First available in Project Euclid: 28 February 2019

Permanent link to this document
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

Subjects
Primary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX] 51E15: Affine and projective planes

Keywords
projective plane collineation group orbit

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


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