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{\bf Cafer Caliskan and G. Eric Moorhouse}
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{\bf Subplanes of Order $3$ in Hughes Planes}
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In this study we show the existence of subplanes of order $3$ in
Hughes planes of order $q^2$, where $q$ is a prime power and $q \equiv
5 \ (mod \ 6)$. We further show that there exist finite partial linear
spaces which cannot embed in any Hughes plane.



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