Previous |  Up |  Next

Article

Keywords:
K-loop; Bol loop; Kikkawa loop; left power alternative loop; 2-divisible loop; derivation
Summary:

References:
[1] Albert A.A.: Quasigroups I. Trans. Amer. Math. Soc. 54 (1943), 507-519. MR 0009962 | Zbl 0063.00039
[2] Artzy R.: Relations between loop identities. Proc. Amer. Math. Soc. 11 (1960), 847-851. MR 0117295
[3] Belousov V.D.: Foundations of the Theory of Quasigroups and Loops. Izdat. Nauka, Moscow, 1967, (Russian). MR 0218483
[4] Bol G.: Gewebe und Gruppen. Math. An. 114 (1937), 414-431. MR 1513147 | Zbl 0016.22603
[5] Bruck R.H.: A Survey of Binary Systems. 2$^{nd}$ ed., Springer-Verlag, Berlin-Heidelberg-New York, 1966. MR 0093552 | Zbl 0141.01401
[6] Burn R.P.: Bol quasi-fields and Pappus' theorem. Math. Z. 105 (1968), 351-364. MR 0230215 | Zbl 0159.49803
[7] Caggegi A.: Nuovi quasicorpi di Bol. Matematiche (Catania) 35 (1980), 241-247. MR 0698746 | Zbl 0525.51008
[8] Choudhury A.C.: Quasi-groups and nonassociative systems. I. Bull. Calcutta Math. Soc. 40 (1948), 183-194. MR 0029385
[9] Fuchs L.: Infinite Abelian Groups. Academic Press, New York-London, 1970. MR 0255673 | Zbl 0338.20063
[10] Funk M., Nagy P.T.: On collineation groups generated by Bol reflections. J. Geom. 48 (1993), 63-78. MR 1242703 | Zbl 0793.51001
[11] Glauberman G.: On loops of odd order. J. Algebra 1 (1964), 374-396. MR 0175991 | Zbl 0123.01502
[12] Goodaire E.G., Robinson D.A.: Semi-direct products and Bol loop. Demonstratio Math. 27 (1994), 573-588. MR 1319403 | Zbl 0831.20095
[13] Karzel H.: Unendliche Dicksonsche Fastkörper. Arch. Math. (Basel) 16 (1965), 247-256. MR 0183668 | Zbl 0131.01701
[14] Karzel H.: Zusammnehänge zwischen Fastbereichen, scharf zweifach transitiven Permutationsgruppen und $2$-Strukturen mit Rechtecksaxiom. Abh. Math. Sem. Univ. Hamburg 32 (1968), 191-206. MR 0240715
[15] Kiechle H.: Lokal endliche Quasikörper. Ph.D. Thesis, Techn. Univ. München, 1990. Zbl 0715.12007
[16] Kiechle H.: Der Kern einer automorphen Ableitung und eine Anwendung auf normale Teilkörper verallgemeinerter André-Systeme. Arch. Math. (Basel) 58 (1992), 514-520. MR 1156585 | Zbl 0725.12006
[17] Kikkawa M.: Geometry of homogeneous Lie loops. Hiroshima Math. J. 5 (1975), 141-179. MR 0383301 | Zbl 0304.53037
[18] Kikkawa M.: On some quasigroups of algebraic models of symmetric spaces III. Mem. Fac. Sci. Shimane Univ. 9 (1975), 7-12. MR 0412316 | Zbl 0322.20035
[19] Kist G.: Theorie der verallgemeinerten kinematischen Räume. Beiträge zur Geometrie und Algebra 14 (1986), TUM-M8611, Habilitationsschrift, Techn. Univ. München. MR 0924326 | Zbl 0636.51012
[20] Kreuzer A.: Beispiele endlicher und unendlicher K-Loops. Resultate Math. 23 (1993), 355-362. MR 1215220 | Zbl 0788.20036
[21] Kreuzer A.: Construction of finite loops of even order. Proc. of the Conference on Nearrings and Nearfields (Fredericton, NB, Canada, 18-24 July, 1993), Y. Fong & al., eds., Kluwer Acad. Press, 1995, pp.169-179. MR 1366476 | Zbl 0838.20079
[22] Kreuzer A.: Inner mappings of Bol loops. Math. Proc. Cambridge Philos. Soc. 123 (1998), 53-57. MR 1474864
[23] Kreuzer A., Wefelscheid H.: On K-loops of finite order. Resultate Math. 25 (1994), 79-102. MR 1262088 | Zbl 0803.20052
[24] Lüneburg H.: Translation Planes. Springer-Verlag, Berlin-Heidelberg-New York, 1980. MR 0572791
[25] Miheev P.O., Sabinin L.V.: Quasigroups and differential geometry. Quasigroups and Loops: Theory and Applications (O. Chein, H.O. Pflugfelder & J.D.H. Smith, eds.), Heldermann Verlag, Berlin, 1990, pp.357-430. MR 1125818 | Zbl 0721.53018
[26] Pflugfelder H.O.: Quasigroups and Loops: Introduction. Heldermann-Verlag, Berlin, 1990. MR 1125767 | Zbl 0715.20043
[27] Robinson D.A.: Bol loops. Trans. Amer. Math. Soc. 123 (1966), 341-354. MR 0194545 | Zbl 0163.02001
[28] Robinson D.A.: Bol quasigroups. Publ. Math. Debrecen 19 (1972), 151-153. MR 0325829
[29] Sabinin L.V., Sabinina L.L., Sbitneva L.V.: On the notion of gyrogroup. Aequationes Math. 56 (1998), 11-17. MR 1628291 | Zbl 0923.20051
[30] Sabinin L.V., Sbitneva L.V.: Half Bol loops. Webs and Quasigroups, Tver Univ. Press, 1994, pp.50-54. MR 1413337 | Zbl 0897.20044
[31] Sharma B.L.: Left loops which satisfy the left Bol identity. Proc. Amer. Math. Soc. 61 (1976), 189-195. MR 0422480
[32] Timm J.: Zur Konstruktion von Fastringen I. Abh. Math. Sem. Univ. Hamburg 35 (1970), 57-74. MR 0276283 | Zbl 0217.06402
[33] Ungar A.A.: The relativistic noncommutative nonassociative group of velocities and the Thomas rotation. Resultate Math. 16 (1989), 168-179. MR 1020224 | Zbl 0693.20067
[34] Ungar A.A.: Weakly associative groups. Resultate Math. 17 (1990), 149-168. MR 1039282 | Zbl 0699.20055
[35] Ungar A.A.: The holomorphic automorphism group of the complex disk. Aequationes Math. 47 (1994), 240-254. MR 1268034 | Zbl 0799.20032
[36] Wähling H.: Theorie der Fastkörper. Thales Verlag, Essen, 1987. MR 0956467
Partner of
EuDML logo