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The α-regular classes of the generalized symmetric group

Published online by Cambridge University Press:  18 May 2009

E. W. Read
E. W. Read
Affiliation:
Pure Mathematics Department, The University College of Wales, Aberystwyth
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The α-regular classes of any finite group G are important since they are those classes on which the projective characters of G with factor set α take non-zero value, and thus a knowledge of the α-regular classes gives the number of irreducible projective representations of G with factor set α (see [4]). Here we look at the particular case of the generalized symmetric group Cm wr Sl. The analogous problem of constructing the irreducible projective representations of Cm wr Sl has been dealt with in [6] by generalizing Clifford's theory of inducing from normal subgroups, but unfortunately, it is not in general possible to determine the irreducible projective characters (and hence the α-regular classes) by this method.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 2 , July 1976 , pp. 144 - 150
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

REFERENCES

1.Davies, J. W. and Morris, A. O., The Schur multiplier of the generalized symmetric group, J. London Math. Soc. (2), 8 (1974), 615–620.CrossRefGoogle Scholar
2.Huppert, B., Endliche Gruppen (Springer-Verlag, 1967).CrossRefGoogle Scholar
3.Kerber, A., Representations of permutation groups, Lecture notes in Mathematics No. 240 (Springer-Verlag, 1971).CrossRefGoogle Scholar
4.Morris, A. O., Projective representations of finite groups, Proceedings of the conference on Clifford Algebras, Matscience, Madras 1971 (1972), 43–86.Google Scholar
5.Read, E. W., On projective representations of the finite reflection groups of type B l and D l, J. London Math. Soc. (2) 10 (1975), 129–142.CrossRefGoogle Scholar
6.Read, E. W., The projective representations of the generalized symmetric group; to appear.Google Scholar
7.Schur, I., Über die Darstetlungen der symmetrischen und der alternierden Gruppe durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 139 (1911), 155–250.CrossRefGoogle Scholar