Historical notes on loop theory
Pflugfelder, Hala Orlik
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000), p. 359-370 / Harvested from Czech Digital Mathematics Library
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This paper deals with the origins and early history of loop theory, summarizing the period from the 1920s through the 1960s.

Publié le : 2000-01-01
Classification:  01A60,  20-03,  20N05 
@article{119169,
     author = {Hala Orlik Pflugfelder},
     title = {Historical notes on loop theory},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {41},
     year = {2000},
     pages = {359-370},
     zbl = {1037.01010},
     mrnumber = {1780877},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119169}
}

Pflugfelder, Hala Orlik. Historical notes on loop theory. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 359-370. http://gdmltest.u-ga.fr/item/119169/

Aczél J. Quasigroups, nets, and nomograms, Adv. in Math. 1 (1965), MR 33 (1967). (1965) | MR 0193174

Albert A.A. Quasigroups. I, Trans. Amer. Math. Soc. 54 (1943), MR 5 (1944). (1943) | MR 0009962 | Zbl 0063.00039

Albert A.A. Quasigroups. II, Trans. Amer. Math. Soc. 55 (1944), MR 6 (1945). (1944) | MR 0010597 | Zbl 0063.00042

Artzy R. Isotopy and parastrophy of quasigroups, Proc. Amer. Math. Soc. 14 (1963). (1963) | MR 0147574 | Zbl 0108.25801

Belousov V.D. Foundations of the Theory of Quasigroups and Loops, Nauka, 1967, MR 36 (1968). | MR 0218483

Baer R. Homogeneity of projective planes, Amer. J. Math. 64 (1942). (1942) | MR 0005629 | Zbl 0060.32207

Blaschke W.; Bol G. Geometrie der Gewebe, Springer-Verlag, 1938. | Zbl 0020.06701

Bol G. Gewebe und Gruppen, Math. Ann. 114 (1937). (1937) | MR 1513147 | Zbl 0016.22603

Bruck R.H. Some results in the theory of quasigroups, Trans. Amer. Math. Soc. 56 (1944), MR 6 (1945). (1944) | MR 0009963 | Zbl 0063.00635

Bruck R.H. Contributions to the Theory of Loops (1946), Trans. Amer. Math. Soc. 60 (1946), MR 8 (1947). (1946) | MR 0017288

Bruck R.H. A Survey of Binary Systems, Springer-Verlag, 1958, MR 29 (1959). | MR 0093552 | Zbl 0141.01401

Etherington I.M.H. Quasigroups and cubic curves, Edinburgh Math. Soc. 14 (1964), MR 33 (1967). (1964) | MR 0195974

Evans T. Homomorphisms of non-associative systems, J. London Math. Soc. 24 (1949), MR 11 (1950). (1949) | MR 0032664

Freudenthal H. Octaven, Ausnahmegruppen und Oktavengeometrie, Utrecht, 1951, MR 13 (1952).

Garrison G.N. Quasi-groups, Ann. of Math. 41 (2) (1940), MR 7 (1946). (1940) | MR 0002150 | Zbl 0024.15005

Hall M. Projective planes, Trans. Amer. Math. Soc. 54 (1943), MR 5 (1944). (1943) | MR 0008892 | Zbl 0060.32209

Hausmann B.A.; Ore O. Theory of quasi-groups, Amer. J. Math. 59 (1937). (1937) | Zbl 0017.39102

Mal'Cev A.I. Analytic loops, Math. Sb. 36 (1955), MR 16 (1955). (1955) | MR 0069190

Manin Yu.I. Cubic hypersurfaces I, Math. USSR-Izv. 2 (1968), MR 38 (1969). (1968) | Zbl 0193.21604

Moufang R. Zur Struktur von Alternativkoerpern, Math. Ann. 110 (1935). (1935) | MR 1512948

Murdoch D.C. Quasi-groups which satisfy certain generalized associative laws, Amer. J. Math. 61 (1939). (1939) | MR 1507391 | Zbl 0020.34702

Pickert G. Projective Ebenen, Springer-Verlag, 1955, 2nd ed. 1975, MR 51 (1976).

Pontryagin L.S. Topologische Gruppen, Teubner, 1957, MR 20 (1959). | Zbl 0265.22001

Robinson D.A. Bol loops, Trans. Amer. Math. Soc. 123 (1966), MR 33 (1967). (1966) | MR 0194545 | Zbl 0163.02001

Sade A. Quasigroupes Parastrophiques, Math. Nachr. 20 (1959), MR 22 (1961). (1959) | MR 0114870 | Zbl 0092.25801

Suschkewitsch A.K. On a generalization of the associative law, Trans. Amer. Math. Soc. 31 (1929). (1929)

Zorn M. Theorie der Alternativen Ringe, Hamb. Abhandl. 8 (1930). (1930)