Abstract

In this paper, it is shown that any projective plane $\Pi$ of order $n\le q^4$, $q$ odd, that admits a group $G\cong PSL\left(3,q\right)$ 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 $\Pi$, respectively. In particular,  if $n\le q^3$, actually, $n=q$, $q^2$ or $q^3$.

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Mathematical Subject Classification 2000

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