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Generators for Simple Groups

Published online by Cambridge University Press:  20 November 2018

Robert Steinberg
Robert Steinberg*
Affiliation:
University of California
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The list of known finite simple groups other than the cyclic, alternating, and Mathieu groups consists of the classical groups which are (projective) unimodular, orthogonal, symplectic, and unitary groups, the exceptional groups which are the direct analogues of the exceptional Lie groups, and certain twisted types which are constructed with the aid of Lie theory (see §§3 and 4 below). In this article, it is proved that each of these groups is generated by two of its elements. It is possible that one of the generators can be chosen of order 2, as is the case for the projective unimodular group (1), or even that one of the generators can be chosen as an arbitrary element other than the identity, as is the case for the alternating groups. Either of these results, if true, would quite likely require methods much more detailed than those used here.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 277 - 283
Copyright
Copyright © Canadian Mathematical Society 1962

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