Geodesic
The Multiplicative Groups of Quasifields
Canadian journal of mathematics, Tome 39 (1987) no. 4, pp. 784-793

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

Let (Q, +, ·) be a finite quasifield of dimension d over its kernel K = GF(q), where q = pk with p a prime and k ≧ 1. (See p. 18-22 and p. 74 of [7] or Section 5 of [9] for the definition of quasifield.) For the remainder of this article we will follow standard conventions and omit, whenever possible, the binary operations + and · in discussing a quasifield. For example, the notation Q will be used in place of the triple (Q, +, ·) and Q* will be used to represent the multiplicative loop (Q − {0}, ·).Let m be a non-zero element of the quasifield Q; the right multiplicative mapping ρm:Q → Q is defined by 1 
Kallaher, Michael J. The Multiplicative Groups of Quasifields. Canadian journal of mathematics, Tome 39 (1987) no. 4, pp. 784-793. doi: 10.4153/CJM-1987-038-x
@article{10_4153_CJM_1987_038_x,
     author = {Kallaher, Michael J.},
     title = {The {Multiplicative} {Groups} of {Quasifields}},
     journal = {Canadian journal of mathematics},
     pages = {784--793},
     year = {1987},
     volume = {39},
     number = {4},
     doi = {10.4153/CJM-1987-038-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-038-x/}
}
TY  - JOUR
AU  - Kallaher, Michael J.
TI  - The Multiplicative Groups of Quasifields
JO  - Canadian journal of mathematics
PY  - 1987
SP  - 784
EP  - 793
VL  - 39
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-038-x/
DO  - 10.4153/CJM-1987-038-x
ID  - 10_4153_CJM_1987_038_x
ER  - 
%0 Journal Article
%A Kallaher, Michael J.
%T The Multiplicative Groups of Quasifields
%J Canadian journal of mathematics
%D 1987
%P 784-793
%V 39
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1987-038-x/
%R 10.4153/CJM-1987-038-x
%F 10_4153_CJM_1987_038_x

[1] 1. Albert, A. A., On the collineation groups of certain non-desarguesian planes, Portugal. Math. 75 (1959), 207–224. Google Scholar

[2] 2. Bruck, R. H. and Bose, R. C., Linear representations of projective planes in projective spaces, J. Algebra 4 (1966), 117–172. Google Scholar

[3] 3. Dembowski, P., Finite geometries (Springer-Verlag, Berlin-Heidelberg-New York, 1968). Google Scholar | DOI

[4] 4. Foulser, D. A., A generalization of Andre's systems, Math. Z. 100 (1967), 380–395. Google Scholar

[5] 5. Hering, C., Zweifach transitive Permutationsgruppen in denen 2 die maximale Anzahl von Fixpunkten von Involutionen ist, Math. Z. 104 (1968), 150–174. Google Scholar

[6] 6. Huppert, B., Zweifach transitive auflôsbare Permutationsgruppen, Math. Z. 68 (1957), 126–150. Google Scholar

[7] 7. Kallaher, M. J., Affine planes with transitive collineation groups, (North Holland, New York-Amsterdam-Oxford, 1982). Google Scholar

[8] 8. Kallaher, M. J. and Ostrom, T. G., Fixed point free linear groups, rank three planes, and Bol quasifields, J. Algebra 18 (1971), 159–178. Google Scholar

[9] 9. Lüneburg, H., Translation planes (Springer-Verlag, Berlin-Heidelberg-New York, 1980). Google Scholar | DOI

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

[11] 11. Passman, D. S., Permutation groups, (Benjamin, New York-Amsterdam, 1968). Google Scholar

[12] 12. Rao, M. L. N., Characterization of Foulser's λ-systems, Proc. Amer. Math. Soc. 24 (1970), 538–544. Google Scholar

Cité par Sources :