Computational Aspects of Representation Theory of Finite Groups II

The classification of the finite simple groups is one of the important achievements of the mathematicians in this century. According to p. 3 of the recent book [16] by Gorenstein, Lyons and Solomon “The existing proof of the classification of the finite simple groups runs to somewhere between 10 000 and 15 000 journal pages, spread across some 500 separate articles by more than 100 mathematicians .... As a result of these various factors, it is extremely difficult for even the most diligent mathematician to obtain a comprehensive picture of the proof by examining the existing literature.” On p. 45 of [16] these authors write: “The most serious problem concerns the sporadic groups, whose development at the time of the completion of the classification theorem was far from satisfactory. The existence and uniqueness of the sporadic groups and the development of their properties form a very elaborate chapter of simple group theory, spread across a large number of journal articles. Moreover, some of the results are unpublished (e.g. Sims’ computer calculations establishing the existence and uniqueness of the Lyons group Ly).Furthermore, until very recently, the two principal sources for properties of the sporadic groups were [5] and [15], Part 1, §5 consisting only of statements of results without proofs.”