Regular permutation sets and loops

Rita Capodaglio

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 3, page 617-628
  • ISSN: 0392-4041

Abstract

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Two suitable composition laws are defined in a regular permutation set in order to find new characterizations of some important classes of loops.

How to cite

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Capodaglio, Rita. "Regular permutation sets and loops." Bollettino dell'Unione Matematica Italiana 6-B.3 (2003): 617-628. <http://eudml.org/doc/195562>.

@article{Capodaglio2003,
abstract = {Two suitable composition laws are defined in a regular permutation set in order to find new characterizations of some important classes of loops.},
author = {Capodaglio, Rita},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {regular permutation sets; right translations; Bol loops; Bruck loops; -loops},
language = {eng},
month = {10},
number = {3},
pages = {617-628},
publisher = {Unione Matematica Italiana},
title = {Regular permutation sets and loops},
url = {http://eudml.org/doc/195562},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Capodaglio, Rita
TI - Regular permutation sets and loops
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/10//
PB - Unione Matematica Italiana
VL - 6-B
IS - 3
SP - 617
EP - 628
AB - Two suitable composition laws are defined in a regular permutation set in order to find new characterizations of some important classes of loops.
LA - eng
KW - regular permutation sets; right translations; Bol loops; Bruck loops; -loops
UR - http://eudml.org/doc/195562
ER -

References

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  2. BRUCK, R. H.- PAIGE, L. J., Loops whose inner mappings are automorphisms, Ann. of Math., 63 (1956), 308-323. Zbl0074.01701MR76779
  3. BURN, R. P., Finite Bol loops, Math. Proc. Camb. Phil. Soc., 84 (1978), 337-389. Zbl0385.20043MR492030
  4. CAPODAGLIO, R., Cappi e Permutazioni, Note di Matem., III (1983), 229-243. MR791347
  5. CAPODAGLIO, R., TWO LOOPS IN THE ABSOLUTE PLANE. TO APPEAR Zbl1088.20038MR2106662
  6. CAPODAGLIO, R.- VERARDI, L., On a Permutation Representation for Finite Loops, Ist. Lomb. (Rend.) A, 124 (1990), 15-22. Zbl0755.20018MR1267845
  7. DORO, S., Simple Moufang loops, Math. Proc. Camb. Phil. Soc., 83 (1978), 377-392. Zbl0381.20054MR492031
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  10. KARZEL, H.- WEFELSHEID, H., Groups with an involutory antiautomorphism and K -loops, application to space-time-world and hyperbolic geometry I, Results Math., 23 (1993), 338-354. Zbl0788.20034MR1215219
  11. KIECHLE, H., K -loops from classical groups over ordered fields, J. Geom., 61 (1998), 105-127. Zbl0904.20051MR1603817
  12. KIECHLE, H., Theory of K -Loops, Springer2002. Zbl0997.20059MR1899153
  13. KIKKAWA, M., Geometry of homogeneous Lie loops, Hiroshima Math. J, 5 (1975), 141-179. Zbl0304.53037MR383301
  14. KREUZER, A., Inner mappings of Bruck loops, Math. Proc. Camb. Phil. Soc., 123 (1998), 53-58. Zbl0895.20052MR1474864
  15. KREUZER, A.- WEFELSCHEID, H., On K -loops of finite order, Results Math., 25 (1994), 79-102. Zbl0803.20052MR1262088
  16. NAGY, P. T.- STRAMBACH, K., Loops in Group Theory and Lie Theory, de Gruyter, Berlin, New York2002. Zbl1050.22001MR1899331
  17. PFLUGFELDER, H. O., Quasigroups and Loops: Introduction, Heldermann, Berlin1990. Zbl0715.20043MR1125767
  18. ROBINSON, D. A., Bol Loops, Trans. Amer. Math. Soc., 123 (1966), 341-354. Zbl0163.02001MR194545
  19. UNGAR, A. A., The relativistic noncommutative nonassociative group of velocities and the Thomas rotation, Results Math., 16 (1989), 168-179. Zbl0693.20067MR1020224
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