Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T07:44:10.077Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Burgoyne, N. and Fong, P.A correction to ‘The Schur multipliers of the Mathieu groups’. Nagoya Math. J. 31 (1968), 297–304.Google Scholar
(2)Conway, J. H. Three lectures on exceptional groups. In Finite simple groups, ed. Powell, M. B. and Higman, G. (Academic Press, 1971).Google Scholar
(3)Coxeter, H. S. M.Twelve points in PG(5, 3) with 95040 self-transformations. Proc. Roy. Soc. London. Ser. A 247 (1958), 279–293.Google Scholar
(4)Haggarty, R. J. and Humphreys, J. F.Projective characters of finite groups. Proc. London Math. Soc. 36 (1978), 176–192.CrossRefGoogle Scholar
(5)Humphreys, J. F.Projective modular representations of finite groups. J. London Math. Soc. (2), 16 (1977), 51–66.CrossRefGoogle Scholar
(6)Humphreys, J. F. Projective modiilar representations of finite groups. II. (To appear.)Google Scholar
(7)James, G. D.The modular characters of the Mathieu groups. J. Algebra, 27 (1973), 57–111.CrossRefGoogle Scholar
(8)Oates, F. H. C. Some topics in the theory of projective representations of finite groups. M.Sc. thesis, University of Liverpool, 1978.Google Scholar
(9)Schur, I.Über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitionen. J. reine angew. Math. 127 (1904), 20–50.Google Scholar
(10)Todd, J. A.A representation of the Mathieu group M 24 as a collineation group. Ann. Mat. Pura. Appl. (4), 71 (1966), 199–238.CrossRefGoogle Scholar