Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-27T02:36:02.350Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite distributive quasigroups

Published online by Cambridge University Press:  24 October 2008

J. D. H. Smith
J. D. H. Smith
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The Bruck-Slaby theorem on nilpotence of commutative Moufang loops may be combined with a theorem of Belousov to give a quick elementary proof of a stronger version of Fischer's Theorem on the solubility of right multiplication groups of finite distributive quasigroups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 1 , July 1976 , pp. 37 - 41
Copyright
Copyright © Cambridge Philosophical Society 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Belousov, V. D.O strukture distributivnih kvazigrupp. Mat. Sbornik 50 (1960), 267–298. MR 22, 11059.Google Scholar
(2)Bruch, R. H.A survey of binary systems (Berlin, Springer, 1971).CrossRefGoogle Scholar
(3)Fischer, B.Distributive Quasigruppen endlicher Ordnung. Math. Z. 83 (1964), 267–303.CrossRefGoogle Scholar
(4)Glauberman, G.On loops of odd order. J. Algebra 1 (1964), 374–396.CrossRefGoogle Scholar
(5)Glavberman, G.On loops of odd order II. J. Algebra 8 (1968), 393–414.CrossRefGoogle Scholar
(6)Manin, Ju. I.Kubičeskie formy (Moskva, Nauka, 1972).Google Scholar
(7)Manin, Ju. I. (trans. Hazewinkel, M.) Cubic forms (Amsterdam, North-Holland, 1974).Google Scholar