Geodesic
Indicator Sets in an Affine Space of any Dimension
Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 211-224

Voir la notice de l'article provenant de la source Cambridge University Press

It is well known that a translation plane can be represented in a vector space over a field F where F is a subfield of the kernel of a quasifield which coordinatizes the plane [1; 2; 4, p.220; 10]. If II is a finite translation plane of order qr (q = pn, p any prime), then II may be represented in V2r(q), the vector space of dimension 2r over GF(q), as follows:(i) The points of II are the vectors in V = V2r(q)(ii) The lines of II are(a) A set of qr + 1 mutually disjoint r-dimensional subspaces of V.(b) All translates of in V.(iii) Incidence is inclusion. 
Sherk, F. A. Indicator Sets in an Affine Space of any Dimension. Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 211-224. doi: 10.4153/CJM-1979-022-6
@article{10_4153_CJM_1979_022_6,
     author = {Sherk, F. A.},
     title = {Indicator {Sets} in an {Affine} {Space} of any {Dimension}},
     journal = {Canadian journal of mathematics},
     pages = {211--224},
     year = {1979},
     volume = {31},
     number = {1},
     doi = {10.4153/CJM-1979-022-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-022-6/}
}
TY  - JOUR
AU  - Sherk, F. A.
TI  - Indicator Sets in an Affine Space of any Dimension
JO  - Canadian journal of mathematics
PY  - 1979
SP  - 211
EP  - 224
VL  - 31
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-022-6/
DO  - 10.4153/CJM-1979-022-6
ID  - 10_4153_CJM_1979_022_6
ER  - 
%0 Journal Article
%A Sherk, F. A.
%T Indicator Sets in an Affine Space of any Dimension
%J Canadian journal of mathematics
%D 1979
%P 211-224
%V 31
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-022-6/
%R 10.4153/CJM-1979-022-6
%F 10_4153_CJM_1979_022_6

[1] 1. André, J., Uber nicht-Desarquessche Ebenen mit transitiver. Translationsgruppe, Math. Zei. 60 (1954), 156–186. Google Scholar

[2] 2. Bruck, R. H. and Bose, R. C., The construction of translation planes from projective spaces, J. Algebr. 1 (1964), 85–102. Google Scholar

[3] 3. Bruen, A., Spreads and a conjecture of Bruck and Bose, J. Algebr. 23 (1972), 519–537. Google Scholar

[4] 4. Dembowski, P., Finite geometries (Springer-Verlag, Berlin, 1968). Google Scholar

[5] 5. Foulser, D. A., Collineation groups of generalized André planes, Can. J. Math. 21 (1969), 358–369. Google Scholar

[6] 6. Hering, C., Eine nicht-desarquessche zweifach transitive affine Ebene der Ordnung 27, Abh. Math. Sem. Hamb. 34 (1969), 203–208. Google Scholar

[7] 7. Lunelburg, H., Die Suzukigruppen und ihre Geometrien (Springer-Verlag, Berlin, 1965). Google Scholar

[8] 8. Maduram, D. M., Matrix representation of translation planes, Geometriae Dedicat. 4 (1975), 485–492. Google Scholar

[9] 9. Ostrom, T. G., A characterization of generalized André planes, Math. Zeit. 110 (1969), 1–9. Google Scholar

[10] 10. Ostrom, T. G., Finite translation planes (Springer-Verlag, Berlin, 1970). Google Scholar

[11] 11. Ostrom, T. G., Classification of finite translation planes, Proceedings of the international conference on projective planes held at Washington State University, April 25-28, 1973 (Washington State University Press, 1973). Google Scholar

[12] 12. Rao, M. L. N. and Rao, K. K., A new flag transitive affine plane of order 27, Proc. of the Amer. Math. Soc. 59 (1976), 337–345. Google Scholar

[13] 13. Sherk, F. A. and Pabst, G., Indicator sets, reguli, and new a class of spreads, Can. J. Math. 29 (1977), 132–154. Google Scholar

Cité par Sources :