Geodesic
Subplanes of order 3 in Hughes planes
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/489
Classification : 51E15, 51A35
Mots-clés : Hughes planes, subplane, partial linear space 
@article{10_37236_489,
     author = {Cafer Caliskan and G. Eric Moorhouse},
     title = {Subplanes of order 3 in {Hughes} planes},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/489},
     zbl = {1210.51007},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/489/}
}
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%A G. Eric Moorhouse
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%J The electronic journal of combinatorics
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Cafer Caliskan; G. Eric Moorhouse. Subplanes of order 3 in Hughes planes. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/489

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