Groups, transversals, and loops
Foguel, Tuval
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000), p. 261-269 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.

Publié le : 2000-01-01
Classification:  20D15,  20D99,  20N05 
@article{119162,
     author = {Tuval Foguel},
     title = {Groups, transversals, and loops},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {41},
     year = {2000},
     pages = {261-269},
     zbl = {1038.20047},
     mrnumber = {1780870},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119162}
}

Foguel, Tuval. Groups, transversals, and loops. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 261-269. http://gdmltest.u-ga.fr/item/119162/

Bruck R.H. A Survey of Binary Systems, Springer-Verlag, 1966. | MR 0093552 | Zbl 0141.01401

Cannon J.; Playoust C. An introduction to MAGMA, University of Sydney, Sydney, 1993.

Conway J.H. A simple construction for the Fischer-Griess monster group, Invent. Math. 79 (1985), 3 513-540. (1985) | MR 0782233 | Zbl 0564.20010

Foguel T. Groups with all cyclic subgroups conjugate-permutable groups, J. Group Theory 2 (1999), 1 47-51. (1999) | MR 1670313 | Zbl 0921.20035

Foguel T. Conjugate-permutable subgroups, J. Algebra 191 (1997), 1 235-239. (1997) | MR 1444498 | Zbl 0920.20024

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

Foguel T.; Ungar A.A. Involutory decomposition of groups into twisted subgroups and subgroups, J. Group Theory 3 (2000), 1 27-46. (2000) | MR 1736515 | Zbl 0944.20053

Griess R.L., Jr. Code loops, J. Algebra 100 (1986), 1 224-234. (1986) | MR 0839580 | Zbl 0589.20051

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

Kepka T.; Niemenmaa M. On multiplication groups of loops, J. Algebra 135 (1990), 112-122. (1990) | MR 1076080 | Zbl 0706.20046

Kepka T.; Phillips J.D. Connected transversals to subnormal subgroups, Comment. Math. Univ. Carolinae 38 (1997), 223-230. (1997) | MR 1455488 | Zbl 0889.20020

Kiechle H. $K$-loops from classical groups over ordered fields, J. Geom. 61 (1998), 1-2 105-127. (1998) | MR 1603817 | Zbl 0904.20051

Kinyon M.K.; Jones O. Loops and semidirect products, Comm. Algebra, submitted. | MR 1772003 | Zbl 0974.20049

Robinson D.J.S. A Course in the Theory of Groups, Springer, New York, 1995. | Zbl 0836.20001

Sabinin L.V.; Sabinina L.L.; Sbitneva L.V. On the notion of gyrogroup, Aequationes Math. 56 (1998), 11-17. (1998) | MR 1628291 | Zbl 0923.20051

Sabinin L.V. On the equivalence of categories of loop and homogeneous spaces, Soviet Math. Dokl. 13 (1972), 4 970-974. (1972)

Ungar A.A. Axiomatic approach to the nonassociative group of relativistic velocities, Found. Phys. Lett. 2 (1989), 199-203. (1989) | MR 0994071