Groups, transversals, and loops

Tuval Foguel

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 2, page 261-269
  • ISSN: 0010-2628

Abstract

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

How to cite

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Foguel, Tuval. "Groups, transversals, and loops." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 261-269. <http://eudml.org/doc/248640>.

@article{Foguel2000,
abstract = {A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.},
author = {Foguel, Tuval},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loops; groups; transversals; loops; groups; transversals},
language = {eng},
number = {2},
pages = {261-269},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Groups, transversals, and loops},
url = {http://eudml.org/doc/248640},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Foguel, Tuval
TI - Groups, transversals, and loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 2
SP - 261
EP - 269
AB - A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.
LA - eng
KW - loops; groups; transversals; loops; groups; transversals
UR - http://eudml.org/doc/248640
ER -

References

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  1. Bruck R.H., A Survey of Binary Systems, Springer-Verlag, 1966. Zbl0141.01401MR0093552
  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. (1985) Zbl0564.20010MR0782233
  4. Foguel T., Groups with all cyclic subgroups conjugate-permutable groups, J. Group Theory 2 (1999), 1 47-51. (1999) Zbl0921.20035MR1670313
  5. Foguel T., Conjugate-permutable subgroups, J. Algebra 191 (1997), 1 235-239. (1997) Zbl0920.20024MR1444498
  6. Foguel T., Ungar A.A., Gyrogroups and the decomposition of groups into twisted subgroups and subgroups, Pacific J. Math., to appear. Zbl1066.20068MR1810204
  7. Foguel T., Ungar A.A., Involutory decomposition of groups into twisted subgroups and subgroups, J. Group Theory 3 (2000), 1 27-46. (2000) Zbl0944.20053MR1736515
  8. Griess R.L., Jr., Code loops, J. Algebra 100 (1986), 1 224-234. (1986) Zbl0589.20051MR0839580
  9. Karzel H., Raum-Zeit-Welt und hyperbolische Geometrie, Beiträge zur Geometrie und Algebra 29 (1994), Technische Universität München, Mathematisches Institut, Munich. Zbl0871.51012MR1323631
  10. Kepka T., Niemenmaa M., On multiplication groups of loops, J. Algebra 135 (1990), 112-122. (1990) Zbl0706.20046MR1076080
  11. Kepka T., Phillips J.D., Connected transversals to subnormal subgroups, Comment. Math. Univ. Carolinae 38 (1997), 223-230. (1997) Zbl0889.20020MR1455488
  12. Kiechle H., K -loops from classical groups over ordered fields, J. Geom. 61 (1998), 1-2 105-127. (1998) Zbl0904.20051MR1603817
  13. Kinyon M.K., Jones O., Loops and semidirect products, Comm. Algebra, submitted. Zbl0974.20049MR1772003
  14. Robinson D.J.S., A Course in the Theory of Groups, Springer, New York, 1995. Zbl0836.20001
  15. Sabinin L.V., Sabinina L.L., Sbitneva L.V., On the notion of gyrogroup, Aequationes Math. 56 (1998), 11-17. (1998) Zbl0923.20051MR1628291
  16. Sabinin L.V., On the equivalence of categories of loop and homogeneous spaces, Soviet Math. Dokl. 13 (1972), 4 970-974. (1972) 
  17. Ungar A.A., Axiomatic approach to the nonassociative group of relativistic velocities, Found. Phys. Lett. 2 (1989), 199-203. (1989) MR0994071

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