Subplanes of Order $3$ in Hughes Planes

Cafer Caliskan, G. Eric Moorhouse


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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