Quasithin groups and the classification of the finite simple groups.

Abstract: The classification of the finite simple groups was a vast project involving hundreds of mathematicians in work covering thousands of journal pages, reaching its climax around 1981.

Unfortunately one part of that work, namely the lengthy classification of "quasithin" groups by Mason, was never published. This gap has recently been filled by the publication in November 2004 (Surveys and Monographs of the AMS, vols. 111 and 112) of a more general classification of quasithin groups by Aschbacher and Smith.

The talk will be expository, including some of the history of the overall classification of simple groups, and indicating the place of the quasithin groups within that project; and will lead up to the more general context involved in the Aschbacher-Smith work.