Hostname: page-component-7dd5485656-dk7s8 Total loading time: 0 Render date: 2025-11-02T18:56:42.447Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple Moufang loops

Published online by Cambridge University Press:  24 October 2008

Stephen Doro
Stephen Doro
Affiliation:
Michigan State University, East Lansing, Michigan 48824
Get access Rights & Permissions [Opens in a new window]

Extract

If H is a Moufang loop, and x ∈ H, there are defined permutations of H, L(x):y ↦ xy and R(x): y ↦ yx. The group Gr (H), generated by these permutations for all choices of x, is called the multiplication group of H. It has a close connexion with the structure of H, as shown, for instance, in the papers of Albert(1). The purpose of this paper is to investigate the correspondence between groups and loops, so that group theoretic results may be applied to determine the structure of Moufang loops.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 3 , May 1978 , pp. 377 - 392
Copyright
Copyright © Cambridge Philosophical Society 1978

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1)Albert, A. A.Quasigroups: I. Trans. Amer. Math. Soc. 54 (1943), 507–519.CrossRefGoogle Scholar
Albert, A. A.Quasigroups: II. Trans. Amer. Math. Soc. 55 (1944), 401–419.CrossRefGoogle Scholar
(2)Aschbacher, M.On finite groups generated by odd transpositions: I. Math. Z. 127 (1972), 45–56;CrossRefGoogle Scholar
Aschbacher, M.On finite groups generated by odd transpositions: II. J. Algebra 26 (1973), 451–491.CrossRefGoogle Scholar
Aschbacher, M.On finite groups generated by odd transpositions: III. J. Algebra 26 (1973), 451–491.CrossRefGoogle Scholar
Aschbacher, M.On finite groups generated by odd transpositions: IV. J. Algebra 26 (1973), 451–491.CrossRefGoogle Scholar
(3)Aschbacher, M. and Hall, M. Jr., Groups generated by a class of elements of order 3. J. Algebra 24 (1973), 591–612.CrossRefGoogle Scholar
(4)Bruck, R. H.A survey of binary systems (Berlin, Gottingen, Heidelberg: Springer-Verlag, 1958).CrossRefGoogle Scholar
(5)Doro, S. Finite symmetric spaces. (To appear.)Google Scholar
(6)Glauberman, G.On loops of odd order: I. J. Algebra 1 (1964), 374–396; II. J. Algebra 8 (1968), 393–414.CrossRefGoogle Scholar
(7)Glauberman, G. and Wright, C.Nilpotence of finite Moufang 2-loops. J. Algebra 8 (1968), 415–417.CrossRefGoogle Scholar
(8)Paige, L. J.A class of simple Moufang loops. Proc. Amer. Math. Soc. 7 (1956), 471–482.CrossRefGoogle Scholar
(9)Shult, E.Some analogues of the Z*-theorem. Proc. Amer. Math. Soc. 17 (1966), 1186–1190.Google Scholar
(10)Thompson, J. G.Non-solvable finite groups all of whose local subgroups are solvable. Bull. Amer. Math. Soc. 74 (1968), 383–437.CrossRefGoogle Scholar