Geodesic
Pseudo-Homogeneous Coordinates for Hughes Planes
Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 330-345

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Among the projective planes, the class of Hughes planes has received much interest, for several good reasons. However, the existing descriptions of these planes are somewhat unsatisfactory. We introduce pseudo-homogeneous coordinates which at the same time are easy to handle and give insight into the action of the group that is generated by all elations of the desarguesian Baer subplane of a Hughes plane. The information about the orbit decomposition is then used to give a description in terms of coset spaces of this group. Finally, we exhibit a non-closing Desargues configuration in terms of coordinates.
DOI : 10.4153/CMB-1996-040-9
Mots-clés : Primary 51A35, secondary 51A25, 51A10, Hughes planes, projective planes, special linear groups, nearfileds, orbit decompositions 
Maier, Peter. Pseudo-Homogeneous Coordinates for Hughes Planes. Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 330-345. doi: 10.4153/CMB-1996-040-9
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     author = {Maier, Peter},
     title = {Pseudo-Homogeneous {Coordinates} for {Hughes} {Planes}},
     journal = {Canadian mathematical bulletin},
     pages = {330--345},
     year = {1996},
     volume = {39},
     number = {3},
     doi = {10.4153/CMB-1996-040-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-040-9/}
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