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Blocks and Normal Subgroups of Finite Groups

Published online by Cambridge University Press:  22 January 2016

W. F. Reynolds
W. F. Reynolds*
Affiliation:
Tufts University
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Let H be a normal subgroup of a finite group G, and let ζ be an (absolutely) irreducible character of H. In [7], Clifford studied the irreducible characters X of G whose restrictions to H contain ζ as a constituent. First he reduced this question to the same question in the so-called inertial subgroup S of ζ in G, and secondly he described the situation in S in terms of certain projective characters of S/H. In section 8 of [10], Mackey generalized these results to the situation where all the characters concerned are projective.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 22 , June 1963 , pp. 15 - 32
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1963

References

[1] Asano, K. and Snoda, K., Zur Théorie der Darstellungen einer endlichen Gruppe durch Kollineationen, Compositio Mathematica vol. 2 (1935), pp. 230–240.Google Scholar
[2] Brauer, R., Number theoretical investigations on groups of finite order, Proceedings of the International Symposium on Algebraic Number Theory, Tokyo, 1956, pp. 55–62.Google Scholar
[3] Brauer, R., Zur Darstellungstheorie der Gruppen endlicher Ordnung. I, Math. Zeit. vol. 63 (1956), pp. 406–444.CrossRefGoogle Scholar
[4] Brauer, R., Zur Darstellungstheorie der Gruppen endlicher Ordnung. II, Math. Zeit. vol. 72 (1959), pp. 25–46.CrossRefGoogle Scholar
[5] Brauer, R. and Nesbitt, C., On the modular characters of groups, Ann. of Math. vol. 42 (1941), pp. 556–590.CrossRefGoogle Scholar
[6] Brauer, R. and Tate, J., On the characters of finite groups, Ann. of Math. vol. 62 (1955), pp. 1–7.CrossRefGoogle Scholar
[7] Clifford, A. H., Representations induced in an invariant subgroup, Ann. of Math. vol. 38 (1937), pp. 533–550.Google Scholar
[8] Fong, P., On the characters of p-solvable groups, Trans. Amer. Math. Soc. vol. 98 (1961), pp. 263–284.Google Scholar
[9] Ito, N., On the degrees of irreducible representations of a finite group, Nagoya Math. J. vol. 3 (1951), pp. 5–6.CrossRefGoogle Scholar
[10] Mackey, G. W., Unitary representations of group extensions. I, Acta Mathematica vol. 99 (1958), pp. 265–311.CrossRefGoogle Scholar
[11] Nagao, H., On the theory of representation of finite groups, Osaka Math. J. vol. 3 (1951), pp. 11–20.Google Scholar
[12] Osima, M., On the representations of groups of finite order, Math. J. of Okayama Univ. vol. 1 (1952), pp. 33–61.Google Scholar
[13] Zassenhaus, H., The Theory of Groups, New York, 1949.Google Scholar