Geodesic
A Note on the Construction of Projective Planes from Groups
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1083-1085

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

André (1) gave a construction for translation planes from abelian groups possessing “congruences” of subgroups. Schwerdtfeger (3) constructed the plane over a field F from the group of substitutions x → ax + b (a, b ∊ F; a ≠ 0). In this note we describe a construction (inspired by Schwerdtfeger's work), from groups, of planes which are duals of near-field planes.If a plane is (l, m)-transitive (cf. 2, p. 67) for some pair of distinct lines l, m, then the central collineations φ with axis m and centre on I may be identified with the “proper” points (that is, points not on I or m) of the plane once an origin O is chosen (not on l or m): 
Kirkpatrick, P. B. A Note on the Construction of Projective Planes from Groups. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1083-1085. doi: 10.4153/CJM-1969-120-5
@article{10_4153_CJM_1969_120_5,
     author = {Kirkpatrick, P. B.},
     title = {A {Note} on the {Construction} of {Projective} {Planes} from {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {1083--1085},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-120-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-120-5/}
}
TY  - JOUR
AU  - Kirkpatrick, P. B.
TI  - A Note on the Construction of Projective Planes from Groups
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 1083
EP  - 1085
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-120-5/
DO  - 10.4153/CJM-1969-120-5
ID  - 10_4153_CJM_1969_120_5
ER  - 
%0 Journal Article
%A Kirkpatrick, P. B.
%T A Note on the Construction of Projective Planes from Groups
%J Canadian journal of mathematics
%D 1969
%P 1083-1085
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-120-5/
%R 10.4153/CJM-1969-120-5
%F 10_4153_CJM_1969_120_5

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

[2] 2. Pickert, G., Projektive Ebenen (Springer, Berlin, 1955). Google Scholar

[3] 3. Schwerdtfeger, H., Projective geometry in the one-dimensional affine group, Can. J. Math. 16 (1964), 683–700. Google Scholar

Cité par Sources :