Abstract

Years ago Daniel Gorenstein began a project for giving an outlin of the (“original”) proof of the classification of the finite simple groups—- publishing in 1982 a general introduction, and in 1983 an outline of the classification of groups of non-characteristic 2 type.

But he could not outline the characteristic 2 type case, in view of the non-publication of Mason’s expected treatment of the quasithin groups. This gap was finally filled by the Aschbacher-Smith volumes published in 2004. In particular this cleared the way for completing Gorenstein’s project.

The talk will describe such a work in progress (status: first draft completed) by Aschbacher, Lyons, Smith, and Solomon.

The discussion will be expository, indicating some underlying principles (a few of which have been emerging in retrospect). There will be some mention of improvements since the original proof, and later/future possible alternative approaches.