Realizations of Loops and Groups defined by short identities

Anthony Donald Keedwell

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 3, page 373-383
  • ISSN: 0010-2628

Abstract

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In a recent paper, those quasigroup identities involving at most three variables and of “length” six which force the quasigroup to be a loop or group have been enumerated by computer. We separate these identities into subsets according to what classes of loops they define and also provide humanly-comprehensible proofs for most of the computer-generated results.

How to cite

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Keedwell, Anthony Donald. "Realizations of Loops and Groups defined by short identities." Commentationes Mathematicae Universitatis Carolinae 50.3 (2009): 373-383. <http://eudml.org/doc/33321>.

@article{Keedwell2009,
abstract = {In a recent paper, those quasigroup identities involving at most three variables and of “length” six which force the quasigroup to be a loop or group have been enumerated by computer. We separate these identities into subsets according to what classes of loops they define and also provide humanly-comprehensible proofs for most of the computer-generated results.},
author = {Keedwell, Anthony Donald},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasigroup identity; loop; group; quasigroup identities; quasigroups; loops; groups; axioms},
language = {eng},
number = {3},
pages = {373-383},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Realizations of Loops and Groups defined by short identities},
url = {http://eudml.org/doc/33321},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Keedwell, Anthony Donald
TI - Realizations of Loops and Groups defined by short identities
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 3
SP - 373
EP - 383
AB - In a recent paper, those quasigroup identities involving at most three variables and of “length” six which force the quasigroup to be a loop or group have been enumerated by computer. We separate these identities into subsets according to what classes of loops they define and also provide humanly-comprehensible proofs for most of the computer-generated results.
LA - eng
KW - quasigroup identity; loop; group; quasigroup identities; quasigroups; loops; groups; axioms
UR - http://eudml.org/doc/33321
ER -

References

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  1. Belousov V.D., Balanced identities in quasigroups, (in Russian), Mat. Sb. (N.S.) 70 (112) (1966), 55--97. Zbl0199.05203MR0202898
  2. Belousov V.D., A theorem on balanced identities, (in Russian), Mat. Issled. 71 (1983), 22--24. Zbl0544.20060MR0699119
  3. Fiala N.C., Short identities implying that a quasigroup is a loop or group, Quasigroups Related Systems 15 (2007), 263--271. MR2383952
  4. Sade A., Entropie demosienne de multigroupoïdes et de quasigroupes, Ann. Soc. Sci. Bruxelles, Sér. I, 73 (1959), 302--309. Zbl0092.25804MR0124255
  5. Taylor M.A., 10.1112/blms/10.3.285, Bull. Lond. Math. Soc. 10 (1978), 285--286. Zbl0408.20056MR0519910DOI10.1112/blms/10.3.285

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