
\titleofpresentation{Simple Locally Finite Groups Of Diagonal Type}

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

%  [Body of abstract goes here.]

It is generally accepted that it is impossible to classify all
countable simple locally finite groups, at least in the conventional
sense of parametrizing the isomorphism types in some reasonable way.
Instead, according to Hartley \cite{thomas-har}, we should look for 
well-behaved classes that can be classified, and try to increase the 
scope of these as much as possible. For example, the simple locally
finite linear groups were explicitly classified in the early 1980s by
several authors \cite{thomas-be,thomas-bo,thomas-hs,thomas-t}; and a little later, the simple locally finite groups of finitary
linear transformations were explicitly classified by Hall \cite{thomas-hall}.
In this talk, I will consider the question of whether a satisfactory
classification exists for the class of simple locally finite
groups of {\em diagonal type\/}; i.e.\ those simple locally finite groups which 
can be expressed diagonal limits of products of
finite alternating groups.



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

\bibitem{thomas-be}
V. V. Belyaev, {\em Locally finite Chevalley groups\/}, in ``Studies
in Group Theory'', Urals Scientific Centre of the Academy of
Sciences of USSR, Sverlovsk, 1984, pp. 39--50 (in Russian).

\bibitem{thomas-bo}
A. V. Borovik, {\em Periodic linear groups of odd characteristic\/},
Dokl. Akad. Nauk. SSSR {\bf 266} (1982), 1289--1291.

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

\bibitem{thomas-hs}
B. Hartley and G. Shute, {\em Monomorphisms and direct limits of finite
groups of Lie type\/}, Quart. J. Math (2) {\bf 35} (1984), 49--71.

\bibitem{thomas-har}
B. Hartley, {\em Simple locally finite groups\/},
in ``Finite and locally finite groups''
(edited by B. Hartley, G. M. Seitz, A. V. Borovik and
R. M. Bryant), Klumer Academic Publ., Dordrecht, 1995,
pp. 1--44.

\bibitem{thomas-t}
S. Thomas, {\em The classification of the simple periodic linear
groups\/}, Arch. Math. {\bf 41} (1983), 103--116.

\end{ourbiblio}

\presenteraddress{Rutgers University}  % The name of a university is fine.

\email{sthomas@math.rutgers.edu}

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

