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.
On the finite projective planes of order up to q^4, q odd, admitting PSL(3,q) as a collineation group
BILIOTTI, Mauro;MONTINARO, Alessandro
2008-01-01
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.File in questo prodotto:
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