Two suitable composition laws are defined in a regular permutation set in order to find new characterizations of some important classes of loops.
Utilizzando insiemi regolari di permutazioni e due operazioni opportunamente definite, si ottengono nuove caratterizzazioni di importanti classi di cappi.
@article{BUMI_2003_8_6B_3_617_0, author = {Rita Capodaglio}, title = {Regular permutation sets and loops}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {6-A}, year = {2003}, pages = {617-628}, zbl = {1119.20057}, mrnumber = {2014823}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2003_8_6B_3_617_0} }
Capodaglio, Rita. Regular permutation sets and loops. Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003) pp. 617-628. http://gdmltest.u-ga.fr/item/BUMI_2003_8_6B_3_617_0/
[1] | MR 93552 | Zbl 0206.30301
, A survey of binary systems, Springer Verlag (1971).[2] Loops whose inner mappings are automorphisms, Ann. of Math., 63 (1956), 308-323. | MR 76779 | Zbl 0074.01701
- ,[3] Finite Bol loops, Math. Proc. Camb. Phil. Soc., 84 (1978), 337-389. | MR 492030 | Zbl 0385.20043
,[4] Cappi e Permutazioni, Note di Matem., III (1983), 229-243. | MR 791347
,[5] TWO LOOPS IN THE ABSOLUTE PLANE. TO APPEAR | MR 2106662 | Zbl 1088.20038
,[6] On a Permutation Representation for Finite Loops, Ist. Lomb. (Rend.) A, 124 (1990), 15-22. | MR 1267845 | Zbl 0755.20018
- ,[7] Simple Moufang loops, Math. Proc. Camb. Phil. Soc., 83 (1978), 377-392. | MR 492031 | Zbl 0381.20054
,[8] Recent developments on absolute geometries and algebraization by Kloops, Discr. Math., 208/209 (1999), 387-409 | MR 1725545 | Zbl 0941.51002
,[9] A Geometric Construction of the -Loop of a Hyperbolic Space, Geom. Dedicata, 58 (1995), 227-236 | MR 1358454 | Zbl 0845.51002
, - ,[10] Groups with an involutory antiautomorphism and -loops, application to space-time-world and hyperbolic geometry I, Results Math., 23 (1993), 338-354. | MR 1215219 | Zbl 0788.20034
- ,[11] -loops from classical groups over ordered fields, J. Geom., 61 (1998), 105-127. | MR 1603817 | Zbl 0904.20051
,[12] | MR 1899153 | Zbl 0997.20059
, Theory of -Loops, Springer2002.[13] Geometry of homogeneous Lie loops, Hiroshima Math. J, 5 (1975), 141-179. | MR 383301 | Zbl 0304.53037
,[14] Inner mappings of Bruck loops, Math. Proc. Camb. Phil. Soc., 123 (1998), 53-58. | MR 1474864 | Zbl 0895.20052
,[15] On -loops of finite order, Results Math., 25 (1994), 79-102. | MR 1262088 | Zbl 0803.20052
- ,[16] | MR 1899331 | Zbl 1050.22001
- , Loops in Group Theory and Lie Theory, de Gruyter, Berlin, New York2002.[17] | MR 1125767 | Zbl 0715.20043
, Quasigroups and Loops: Introduction, Heldermann, Berlin1990.[18] Bol Loops, Trans. Amer. Math. Soc., 123 (1966), 341-354. | MR 194545 | Zbl 0163.02001
,[19] The relativistic noncommutative nonassociative group of velocities and the Thomas rotation, Results Math., 16 (1989), 168-179. | MR 1020224 | Zbl 0693.20067
,[20] Weakly associative groups, Results Math., 17 (1990), 149-168. | MR 1039282 | Zbl 0699.20055
, - , Gruppi corpi equazioni, Feltrinelli (1963).