
%  When you are satisfied with your abstract, please delete everything
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\titleofpresentation{Locally finite simple Moufang loops}

\presenter{J. I. Hall}  %  Name just one speaker, please; collaborators
			%  can be credited in the body of the abstract.

%  [Body of abstract goes here.]

A Moufang loop is a binary system close to a group but
satifying only a weak form of the associative law.
Doro and Glauberman \cite{doro,glauberman} observed that there
is a direct connection between simple Moufang loops and simple
groups with triality. Using this correspondence, Liebeck
\cite{liebeck} proved that nonassociative finite simple
Moufang loops arise from split octonian algebras over finite 
fields. The techniques used in the study
of locally finite simple groups (say, \cite{istanbul,annals})
can then be used to prove that Liebeck's
result remains true with ``locally finite'' in place of 
``finite.''


\begin{ourbiblio}{99}  %  Delete this environment if you
		       %  aren't giving a bibliography.

\bibitem{doro} 
S. {Doro,} Simple Moufang loops,  Math. Proc. Cambridge Philos. 
Soc. {\bf  83} (1978), 377--392.

\bibitem{glauberman}
G. {Glauberman,} On loops of odd order, I,  J. Algebra {\bf  1} (1964), 374--396; II,  J. Algebra {\bf  8} (1968), 393--414.

\bibitem{istanbul}
J.I. Hall, Locally finite simple groups of finitary linear transformations, in: {\em Finite and locally finite groups 
(Istanbul, 1994)}, eds.: B. Hartley, G.M. Seitz, A.V. Borovik, 
and R.M. Bryant,
147--188, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., {\bf 471},
Kluwer Acad. Publ., Dordrecht, 1995.

\bibitem{annals} J.I. Hall, Periodic simple groups of finitary linear
transformations.  Ann. of Math. (2)  {\bf 163}  (2006),  445--498.

\bibitem{liebeck} 
M.W. Liebeck, The classification of finite simple Moufang loops,
Math. Proc. Cambridge Philos. Soc. {\bf 102} (1987), 33--47.

\end{ourbiblio}

\presenteraddress{Michigan State University, East Lansing, MI 48824 USA}  % The name of a university is fine.

\email{jhall@math.msu.edu}

\web{www.math.msu.edu/~jhall/}  % Those without homepages should delete this.

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