Abstract
In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both within group theory and outside. The purpose of this article is to consider the theory of finite permutation groups with the assumption that the finite simple groups are known, and to examine questions such as: which problems are solved or solvable under this assumption, and what important problems remain?
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