Twelve Sporadic Groups

The finite simple groups come in several infinite families (alternating groups and the groups of Lie type) plus 26 sporadic groups. The sporadic groups, discovered between 1861 and 1975, exist because of special combinatorial or arithmetic circumstances. A single theme does not capture them all. Nevertheless, certain themes dominate. The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. A leisurely and rigorous study of two of their three generations is the purpose of this book. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.