Geodesic
Reidemeister Projective Planes
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1459-1464

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

By a Reidemeister plane we mean a projective plane having the property that every ternary ring coordinatizing it has associative addition. Finite Reidemeister planes have been investigated by Gleason (2), Liineburg (6), and Kegel and Luneburg (4). In the first paper, Gleason proved that if the order of the plane is a prime power, then it is Desarguesian. Luneburg showed that this is still true if the order is not 60. In the third paper, this last restriction is removed. For infinite planes, the only result is the following theorem due to Pickert (7, p. 301). 
Kallaher, Michael J. Reidemeister Projective Planes. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1459-1464. doi: 10.4153/CJM-1968-147-1
@article{10_4153_CJM_1968_147_1,
     author = {Kallaher, Michael J.},
     title = {Reidemeister {Projective} {Planes}},
     journal = {Canadian journal of mathematics},
     pages = {1459--1464},
     year = {1968},
     volume = {20},
     number = {1},
     doi = {10.4153/CJM-1968-147-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-147-1/}
}
TY  - JOUR
AU  - Kallaher, Michael J.
TI  - Reidemeister Projective Planes
JO  - Canadian journal of mathematics
PY  - 1968
SP  - 1459
EP  - 1464
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-147-1/
DO  - 10.4153/CJM-1968-147-1
ID  - 10_4153_CJM_1968_147_1
ER  - 
%0 Journal Article
%A Kallaher, Michael J.
%T Reidemeister Projective Planes
%J Canadian journal of mathematics
%D 1968
%P 1459-1464
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-147-1/
%R 10.4153/CJM-1968-147-1
%F 10_4153_CJM_1968_147_1

[1] 1. Bruck, R. H., A survey of'binary systems (Springer-Verlag, Berlin, 1958).10.1007/978-3-662-35338-7 Google Scholar | DOI

[2] 2. Gleason, A. M., Finite Fano planes, Amer. J. Math. 78 (1956), 797–807. Google Scholar

[3] 3. Hall, Marshall Jr., The theory of groups (Macmillan, New York, 1959). Google Scholar

[4] 4. Kegel, Otto H. and Lùneburg, Heinz, Ûber die Reidemeisterbedingung. II, Arch. Math. 14 1963), 7–10. Google Scholar

[5] 5. Lüneburg, Heinz, Über die beiden kleinen Satze von Pappos, Arch. Math. 11 (1960), 339–341. Google Scholar

[6] 6. Lüneburg, Heinz, Über die Heine Reidemeisterbedingung, Arch. Math. 12 (1961), 382–384. Google Scholar

[7] 7. Pickert, Gunter, Projektive Ebenen (Springer-Verlag, Berlin, 1955).10.1007/978-3-662-00110-3 Google Scholar | DOI

Cité par Sources :