Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Isotopy of abelian quasigroups


Author: Phullendu Das
Journal: Proc. Amer. Math. Soc. 63 (1977), 317-323
MSC: Primary 22A25; Secondary 20N05
MathSciNet review: 0498949
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that every abelian quasigroup possesses a class of isomorphic principal isotopes which are commutative groups. Also it is indicated how the corresponding result for topological quasigroups can be utilised to obtain results for abelian topological quasigroups from analogous results for commutative topological groups.


References [Enhancements On Off] (What's this?)

  • [1] J. Aczél, Lectures on functional equations and their applications, Mathematics in Science and Engineering, Vol. 19, Academic Press, New York-London, 1966. Translated by Scripta Technica, Inc. Supplemented by the author. Edited by Hansjorg Oser. MR 0208210
  • [2] Richard Hubert Bruck, A survey of binary systems, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge, Heft 20. Reihe: Gruppentheorie, Springer Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0093552
  • [3] Phullendu Das, A note on homotopy and isotopy of topological groupoids, Progr. Math. (Allahabad) 1 (1967), no. 2, 20–27. MR 0230834
  • [4] -, Topological quasigroups, Ph.D. Thesis, Univ. of Calcutta, 1968.
  • [5] Karl Heinrich Hofmann, Topologische Loops, Math. Z. 70 (1958), 13–37 (German). MR 0102572
  • [6] D. C. Murdoch, Quasi-Groups Which Satisfy Certain Generalized Associative Laws, Amer. J. Math. 61 (1939), no. 2, 509–522. MR 1507391, 10.2307/2371517

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22A25, 20N05

Retrieve articles in all journals with MSC: 22A25, 20N05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0498949-4
Article copyright: © Copyright 1977 American Mathematical Society