On the Degrees of Irreducible Representations of a Finite Group

Noboru Itô

doi:10.1017/S0027763000012162

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In 1896 G. Frobenius proved: the degree of any (absolutely) irreducible representation of a finite group divides its order. This theorem was improved by I. Schur in 1904 as follows: the degree of any irreducible representation of a finite group divides the index of its centre.

References

¹⁾ Über die Primfaktoren der Gruppendeterminante, Sitzb. Berlin, S. 1343.

²⁾ Über die Darstellung der endlichen Gruppen durch gebrochene lineare. Substitutionen, J. für Math. 127, S. 20.

³⁾ Neue Begründung der Théorie der Gruppencharaktere, Sitzb. Berlin (1905), S. 406.

⁴⁾ Über Gruppen linearer Substitutionen mit Koeffizienten aus einem algebraischen Zahlkörper, Math. Ann. 71 (1912) S. 355.

⁵⁾ Finite Collineation Groups, Chapter IV, Chicago (1917).

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