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The projective characters of the Mathieu group M12 and of its automorphism group

Published online by Cambridge University Press:  24 October 2008

J. F. Humphreys
J. F. Humphreys
Affiliation:
University of Liverpool
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Extract

In (1), Burgoyne and Fong have shown that the Schur multiplier of the Mathieu group M12 is of order 2. It is shown in Theorem 2·4 that the Schur multiplier of Aut M12, the automorphism group of M12, is also of order 2. It is therefore possible to choose a complex 2-cocycle α of Aut M12, taking only the values 1 and − 1, such that the cohomology class of α is of order 2 and the cohomology class of the restriction of α to M12 is of order 2. The characters of the irreducible α-projective representations of Aut M12 are calculated in § 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 3 , May 1980 , pp. 401 - 412
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

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