The Known Simple Groups

  • Daniel Gorenstein
Part of the The University Series in Mathematics book series (USMA)


In this chapter we give a brief account of the known simple groups. These include the trivial groups of prime order, the alternating groups of degree at least 5, the groups of Lie type, and the 26 sporadic groups. The groups of Lie type are analogues over finite fields of the complex Lie groups, and they constitute the broadest category of known simple groups. The finite case involves a few more “types” than in the complex case; in particular, the family of Suzuki groups and the two families of Ree have no direct complex analogues. The groups of Lie type will be described in Section 2.1, the balance of the chapter being devoted to the sporadic groups.


Conjugacy Class Simple Group Permutation Group Chevalley Group Character Table 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1982

Authors and Affiliations

  • Daniel Gorenstein
    • 1
  1. 1.Rutgers, The State University of New JerseyNew BrunswickUSA

Personalised recommendations