The classification of the finite simple groups.

*(English)*Zbl 0965.20009This article on the classification of finite simple groups is directed towards a broad audience. The author poses some natural questions connected with finite groups and in particular with finite simple groups. He explains in a lucid way why these questions have particular answers. For instance he compares the classification of semisimple Lie algebras with the classification of finite simple groups and points out why for groups we can not expect an elegant classification proof as in the case of Lie algebras. He explains why the difficulty of the classification proof for finite simple groups on the other hand is the reason that this result is so eminently useful. Finally, the author gives some aspects of present activity connected with the classification of simple groups. In particular, he describes efforts in simplifying and solidifying the classification proof. This article is a pleasure to read and is recommended to anyone who is interested to get a first impression of the classification of finite simple groups.

Reviewer: U.Dempwolff (Kaiserslautern)