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Construction of a family of Moufang loops

Published online by Cambridge University Press:  10 April 2007

ROBERT T. CURTIS
ROBERT T. CURTIS*
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT. e-mail: R.T.Curtis@bham.ac.uk
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Abstract

This paper is an excerpt from a Rayleigh essay submitted at the University of Cambridge in January 1970. We reproduce it now as it gives a general construction of a family of Moufang loops to which all bar one of the finite subloops of the Cayley algebra belong. These subloops were classified up to isomorphism in the original essay, but are classified up to equivalence under the action of the group of symmetries of in Boddington and Rumynin [1]. Explicitly, given a group G with an element a such that a2=1 in its centre, we construct a Moufang group in which G has index 2. will be non-associative unless G is abelian.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 2 , March 2007 , pp. 233 - 237
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

REFERENCES

[1] Boddington, P. and Rumynin, D.. On Curtis' theorem about finite octonionic loops. (2005) manuscript.Google Scholar
[2] Bruck, R. H.. A Survey of Binary Systems (Springer-Verlag, 1958).CrossRefGoogle Scholar
[3] Bruck, R. H.. Some theorems on Moufang loops. Math. Z. (1960), 73, 59–78.CrossRefGoogle Scholar
[4] Coxeter, H. S. M. and Moser, W. O. J.. Generators and Relations for Discrete Groups, 4th ed. (Springer-Verlag, 1980).CrossRefGoogle Scholar
[5] Curtis, R. T.. A Classification and Investigation of the Finite Subloops of the Cayley-Dickson Algebra. Essay submitted for the Smith and Rayleigh Prizes (University of Cambridge, 1970).Google Scholar
[6] McKay, J.. Graphs, singularities and finite groups. In Santa Cruz conference on finite groups. Proc. Symp. Pure Math. 37 (1980), 183–186.CrossRefGoogle Scholar