Geodesic
The Group of the Quadratic Residue Tournament
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 51-54

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

A tournament Tn is a set of n nodes a 1a 2, ..., an such that every pair (ai , aj ) of distinct nodes is joined by exactly one of the oriented edges or . If is in Tn , then we say that ai dominates aj and write ai → aj .The (automorphism) group G(Tn ) of a tournament Tn is the group of all permutations φ of the nodes of Tn such that φ(a)→φ(b) if and only if a → b. It is known [9] that there exist tournaments whose group is abstractly isomorphic to a given group H if and only if H has odd order; thus all tournament groups are solvable, by the Feit-Thompson Theorem [7]. 
Goldberg, Myron. The Group of the Quadratic Residue Tournament. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 51-54. doi: 10.4153/CMB-1970-010-8
@article{10_4153_CMB_1970_010_8,
     author = {Goldberg, Myron},
     title = {The {Group} of the {Quadratic} {Residue} {Tournament}},
     journal = {Canadian mathematical bulletin},
     pages = {51--54},
     year = {1970},
     volume = {13},
     number = {1},
     doi = {10.4153/CMB-1970-010-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-010-8/}
}
TY  - JOUR
AU  - Goldberg, Myron
TI  - The Group of the Quadratic Residue Tournament
JO  - Canadian mathematical bulletin
PY  - 1970
SP  - 51
EP  - 54
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-010-8/
DO  - 10.4153/CMB-1970-010-8
ID  - 10_4153_CMB_1970_010_8
ER  - 
%0 Journal Article
%A Goldberg, Myron
%T The Group of the Quadratic Residue Tournament
%J Canadian mathematical bulletin
%D 1970
%P 51-54
%V 13
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-010-8/
%R 10.4153/CMB-1970-010-8
%F 10_4153_CMB_1970_010_8

[1] 1. Alspach, B., Goldberg, M. and Moon, J. W., The group of the composition of two tournaments, Math. Magazine 41 (1968), 77-90. Google Scholar

[2] 2. Assmus, E. F. Jr. and Mattson, H. F. Jr., Research to develop the algebraic theory of codes. AFCRL-68-0478, Scientific Report, Air Force Cambridge Research Laboratory, Bedford, Mass., Sept., 1968. Google Scholar

[3] 3. Dembowski, P., Finite geometries, Springer-Verlag, 1968. Google Scholar

[4] 4. Dixon, J. D., The fitting subgroup of a linear solvable group, Australian Math. Soc. J. 7 (1967), 417-424. Google Scholar

[5] 5. Dixon, J. D., The maximum order of the group of a tournament, Canad. Math. Bull. 10 (1967), 503-505. Google Scholar

[6] 6. Dixon, J. D., The solvable length of a solvable linear group, Math. Z. 107 (1968), 151-158. Google Scholar

[7] 7. Feit, W. and Thompson, J. G., The solvability of groups of odd order, Pac. J. Math. 13 (1963), 775-1029. Google Scholar

[8] 8. Frucht, R., Die Gruppe des Petersenschen Graphen und des Katensysterne der regular en Polyeder, Comment. Math. Helv. 69 (1937), 217-223. Google Scholar

[9] 9. Moon, J. W., Tournaments with a given automorphism group, Can. J. Math. 16 (1964), 485-489. Google Scholar

[10] 10. Moon, J. W., Topics on Tournaments, Holt, Rinehart and Winston, 1968. Google Scholar

[11] 11. Ore, O., Theory of Graphs, A. M. S. Colloq. Pub., Providence, 1962. Google Scholar

[12] 12. Passman, D. S., P-solvable doubly transitive permutation groups, Pac. J. Math. 26 (1968). 555-577. Google Scholar

[13] 13. Passman, D. S., Permutation groups, Benjamin, 1968. Google Scholar

[14] 14. Scott, W. R., Group theory, Prentice Hall, 1964. Google Scholar

[15] 15. Wielandt, H., Finite permutation groups, Academic Press, 1964. Google Scholar

Cité par Sources :