Historical notes on loop theory

Hala Orlik Pflugfelder

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 2, page 359-370
  • ISSN: 0010-2628

Abstract

top
This paper deals with the origins and early history of loop theory, summarizing the period from the 1920s through the 1960s.

How to cite

top

Pflugfelder, Hala Orlik. "Historical notes on loop theory." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 359-370. <http://eudml.org/doc/248577>.

@article{Pflugfelder2000,
abstract = {This paper deals with the origins and early history of loop theory, summarizing the period from the 1920s through the 1960s.},
author = {Pflugfelder, Hala Orlik},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasigroup theory; loop theory; history; quasigroup theory; loop theory; history},
language = {eng},
number = {2},
pages = {359-370},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Historical notes on loop theory},
url = {http://eudml.org/doc/248577},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Pflugfelder, Hala Orlik
TI - Historical notes on loop theory
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 2
SP - 359
EP - 370
AB - This paper deals with the origins and early history of loop theory, summarizing the period from the 1920s through the 1960s.
LA - eng
KW - quasigroup theory; loop theory; history; quasigroup theory; loop theory; history
UR - http://eudml.org/doc/248577
ER -

References

top
  1. Aczél J., Quasigroups, nets, and nomograms, Adv. in Math. 1 (1965), MR 33 (1967). (1965) MR0193174
  2. Albert A.A., Quasigroups. I, Trans. Amer. Math. Soc. 54 (1943), MR 5 (1944). (1943) Zbl0063.00039MR0009962
  3. Albert A.A., Quasigroups. II, Trans. Amer. Math. Soc. 55 (1944), MR 6 (1945). (1944) Zbl0063.00042MR0010597
  4. Artzy R., Isotopy and parastrophy of quasigroups, Proc. Amer. Math. Soc. 14 (1963). (1963) Zbl0108.25801MR0147574
  5. Belousov V.D., Foundations of the Theory of Quasigroups and Loops, Nauka, 1967, MR 36 (1968). MR0218483
  6. Baer R., Homogeneity of projective planes, Amer. J. Math. 64 (1942). (1942) Zbl0060.32207MR0005629
  7. Blaschke W., Bol G., Geometrie der Gewebe, Springer-Verlag, 1938. Zbl0020.06701
  8. Bol G., Gewebe und Gruppen, Math. Ann. 114 (1937). (1937) Zbl0016.22603MR1513147
  9. Bruck R.H., Some results in the theory of quasigroups, Trans. Amer. Math. Soc. 56 (1944), MR 6 (1945). (1944) Zbl0063.00635MR0009963
  10. Bruck R.H., Contributions to the Theory of Loops (1946), Trans. Amer. Math. Soc. 60 (1946), MR 8 (1947). (1946) MR0017288
  11. Bruck R.H., A Survey of Binary Systems, Springer-Verlag, 1958, MR 29 (1959). Zbl0141.01401MR0093552
  12. Etherington I.M.H., Quasigroups and cubic curves, Edinburgh Math. Soc. 14 (1964), MR 33 (1967). (1964) MR0195974
  13. Evans T., Homomorphisms of non-associative systems, J. London Math. Soc. 24 (1949), MR 11 (1950). (1949) MR0032664
  14. Freudenthal H., Octaven, Ausnahmegruppen und Oktavengeometrie, Utrecht, 1951, MR 13 (1952). 
  15. Garrison G.N., Quasi-groups, Ann. of Math. 41 (2) (1940), MR 7 (1946). (1940) Zbl0024.15005MR0002150
  16. Hall M., Projective planes, Trans. Amer. Math. Soc. 54 (1943), MR 5 (1944). (1943) Zbl0060.32209MR0008892
  17. Hausmann B.A., Ore O., Theory of quasi-groups, Amer. J. Math. 59 (1937). (1937) Zbl0017.39102
  18. Mal'cev A.I., Analytic loops, Math. Sb. 36 (1955), MR 16 (1955). (1955) MR0069190
  19. Manin Yu.I., Cubic hypersurfaces I, Math. USSR-Izv. 2 (1968), MR 38 (1969). (1968) Zbl0193.21604
  20. Moufang R., Zur Struktur von Alternativkoerpern, Math. Ann. 110 (1935). (1935) MR1512948
  21. Murdoch D.C., Quasi-groups which satisfy certain generalized associative laws, Amer. J. Math. 61 (1939). (1939) Zbl0020.34702MR1507391
  22. Pickert G., Projective Ebenen, Springer-Verlag, 1955, 2nd ed. 1975, MR 51 (1976). 
  23. Pontryagin L.S., Topologische Gruppen, Teubner, 1957, MR 20 (1959). Zbl0265.22001
  24. Robinson D.A., Bol loops, Trans. Amer. Math. Soc. 123 (1966), MR 33 (1967). (1966) Zbl0163.02001MR0194545
  25. Sade A., Quasigroupes Parastrophiques, Math. Nachr. 20 (1959), MR 22 (1961). (1959) Zbl0092.25801MR0114870
  26. Suschkewitsch A.K., On a generalization of the associative law, Trans. Amer. Math. Soc. 31 (1929). (1929) 
  27. Zorn M., Theorie der Alternativen Ringe, Hamb. Abhandl. 8 (1930). (1930) 

NotesEmbed ?

top

You must be logged in to post comments.