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Keywords:
loops; groups; transversals
Summary:
A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.
References:
[1] Bruck R.H.: A Survey of Binary Systems. Springer-Verlag, 1966. MR 0093552 | Zbl 0141.01401
[2] Cannon J., Playoust C.: An introduction to MAGMA. University of Sydney, Sydney, 1993.
[3] Conway J.H.: A simple construction for the Fischer-Griess monster group. Invent. Math. 79 (1985), 3 513-540. MR 0782233 | Zbl 0564.20010
[4] Foguel T.: Groups with all cyclic subgroups conjugate-permutable groups. J. Group Theory 2 (1999), 1 47-51. MR 1670313 | Zbl 0921.20035
[5] Foguel T.: Conjugate-permutable subgroups. J. Algebra 191 (1997), 1 235-239. MR 1444498 | Zbl 0920.20024
[6] Foguel T., Ungar A.A.: Gyrogroups and the decomposition of groups into twisted subgroups and subgroups. Pacific J. Math., to appear. MR 1810204 | Zbl 1066.20068
[7] Foguel T., Ungar A.A.: Involutory decomposition of groups into twisted subgroups and subgroups. J. Group Theory 3 (2000), 1 27-46. MR 1736515 | Zbl 0944.20053
[8] Griess R.L., Jr.: Code loops. J. Algebra 100 (1986), 1 224-234. MR 0839580 | Zbl 0589.20051
[9] Karzel H.: Raum-Zeit-Welt und hyperbolische Geometrie. Beiträge zur Geometrie und Algebra 29 (1994), Technische Universität München, Mathematisches Institut, Munich. MR 1323631 | Zbl 0871.51012
[10] Kepka T., Niemenmaa M.: On multiplication groups of loops. J. Algebra 135 (1990), 112-122. MR 1076080 | Zbl 0706.20046
[11] Kepka T., Phillips J.D.: Connected transversals to subnormal subgroups. Comment. Math. Univ. Carolinae 38 (1997), 223-230. MR 1455488 | Zbl 0889.20020
[12] Kiechle H.: $K$-loops from classical groups over ordered fields. J. Geom. 61 (1998), 1-2 105-127. MR 1603817 | Zbl 0904.20051
[13] Kinyon M.K., Jones O.: Loops and semidirect products. Comm. Algebra, submitted. MR 1772003 | Zbl 0974.20049
[14] Robinson D.J.S.: A Course in the Theory of Groups. Springer, New York, 1995. Zbl 0836.20001
[15] 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
[16] Sabinin L.V.: On the equivalence of categories of loop and homogeneous spaces. Soviet Math. Dokl. 13 (1972), 4 970-974.
[17] Ungar A.A.: Axiomatic approach to the nonassociative group of relativistic velocities. Found. Phys. Lett. 2 (1989), 199-203. MR 0994071
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