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The Schur Multipliers of the Mathieu Groups1)

Published online by Cambridge University Press:  22 January 2016

N. Burgoyne  and
P. Fong
N. Burgoyne
Affiliation:
Department of Mathematics University of California Berkeley, California University of Illinois, Chicago, Illinois
P. Fong
Affiliation:
Department of Mathematics University of California Berkeley, California University of Illinois, Chicago, Illinois
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The Mathieu groups are the finite simple groups M11, M12, M22, M23, M24 given originally as permutation groups on respectively 11, 12, 22, 23, 24 symbols. Their definition can best be found in the work of Witt [1]. Using a concept from Lie group theory we can describe the Schur multiplier of a group as the center of a “simply-connected” covering of that group. A precise definition will be given later. We also mention that the Schur multiplier of a group is the second cohomology group of that group acting trivially on the complex roots of unity. The purpose of this paper is to determine the Schur multipliers of the five Mathieu groups.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 733 - 745
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

Footnotes

2)

Alfred P. Sloan Foundation Fellow.

1)

This work was partially supported by the Office of Naval Research (Contract Nonr 3656-09) and by the National Science Foundation (Contract NSF GP-1610).

References

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