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Simple Moufang loops

Published online by Cambridge University Press:  24 October 2008

Stephen Doro
Stephen Doro
Affiliation:
Michigan State University, East Lansing, Michigan 48824
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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.

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

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References

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