On the Degrees of Irreducible Representations of a Finite Group

Noboru Itô

doi:10.1017/S0027763000012162

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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).

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Huppert, Bertram 1957. Lineare aufl�sbare Gruppen. Mathematische Zeitschrift, Vol. 67, Issue. 1, p. 479.

Solomon, Louis 1961. On the sum of the elements in the character table of a finite group.. Proceedings of the American Mathematical Society, Vol. 12, Issue. 6, p. 962.

Ito, Noboru 1962. A Note onSL r (q). Archiv der Mathematik, Vol. 13, Issue. 1, p. 331.

Coleman, D. B. 1962. Finite groups with isomorphic group algebras. Transactions of the American Mathematical Society, Vol. 105, Issue. 1, p. 1.

Reynolds, W. F. 1963. Blocks and Normal Subgroups of Finite Groups. Nagoya Mathematical Journal, Vol. 22, Issue. , p. 15.

Huppert, Bertram 1966. Zur Gasch�tzschen Theorie der Formationen. Mathematische Annalen, Vol. 164, Issue. 2, p. 133.

Dade, E. C. 1968. Degrees of modular irreducible representations ofp-solvable groups. Mathematische Zeitschrift, Vol. 104, Issue. 2, p. 141.

Janko, Zvonimir 1968. A characterization of the Mathieu simple groups, I. Journal of Algebra, Vol. 9, Issue. 1, p. 1.

Keller, Gordon 1968. Concerning the degrees of irreducible characters. Mathematische Zeitschrift, Vol. 107, Issue. 3, p. 221.

JANKO, ZVONIMIR 1969. Symposia Mathematica. p. 25.

Burde, Gerhard 1970. Darstellungen von Knotengruppen und eine Knoteninvariante. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 35, Issue. 1-2, p. 107.

Hafer, Eberhard 1974. Darstellungen von Verkettungsgruppen und eine Invariante des Verkettungstups. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 40, Issue. 1, p. 176.

Fong, Paul and Srinivasan, Bhama 1982. The blocks of finite general linear and unitary groups. Inventiones Mathematicae, Vol. 69, Issue. 1, p. 109.

Karpilovsky, G. 1985. Dimensions of irreducible modules over twisted group algebras. Archiv der Mathematik, Vol. 45, Issue. 4, p. 323.

1987. Representations of Finite Groups. p. 407.

Manz, Olaf 1987. On the Modular Version of Ito’s Theorem on Character Degrees for Groups of Odd Order. Nagoya Mathematical Journal, Vol. 105, Issue. , p. 109.

Carlson, Jon F. and Roggenkamp, Klaus W. 1988. It�'s Theorem and character degrees revisited. Archiv der Mathematik, Vol. 50, Issue. 3, p. 214.

Dowker, J. S. and Jadhav, S. P. 1989. Symmetry breaking by Wilson loops in gauge field theory. Physical Review D, Vol. 39, Issue. 4, p. 1196.

Chillag, David and Herzog, Marcel 1990. On the length of the conjugacy classes of finite groups. Journal of Algebra, Vol. 131, Issue. 1, p. 110.

Huppert, Bertram 1991. Representation Theory of Finite Groups and Finite-Dimensional Algebras. p. 17.

Download full list

Article contents

On the Degrees of Irreducible Representations of a Finite Group

Extract

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests