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The Mathieu Groups

Published online by Cambridge University Press:  20 November 2018

R. G. Stanton
R. G. Stanton*
Affiliation:
The University of Toronto
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An enumeration of known simple groups has been given by Dickson [17]; to this list, he made certain additions in later papers [15], [16]. However, with but five exceptions, all known simple groups fall into infinite families; these five unusual simple groups were discovered by Mathieu [21], [22] and, after occasioning some discussion [20], [23], [27], were relegated to the position, which they still hold, of freakish groups without known relatives. Further interest is attached to these Mathieu groups in virtue of their providing the only known examples (other than the trivial examples of the symmetric and alternating groups) of quadruply and quintuply transitive permutation groups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 164 - 174
Copyright
Copyright © Canadian Mathematical Society 1951

References

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