The average degree of an irreducible character of a finite group

Given a finite group G , we write acd( G ) to denote the average of the degrees of the irreducible characters of G . We show that if acd( G ) ≤ 3, then G is solvable. Also, if acd( G ) < 3/2, then G is supersolvable, and if acd( G ) < 4/3, then G is nilpotent.

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Veröffentlicht in:	Israel journal of mathematics 2013-10, Vol.197 (1), p.55-67
Hauptverfasser:	Isaacs, I. M., Loukaki, Maria, Moretó, Alexander
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Analysis Applications of Mathematics Group Theory and Generalizations Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Given a finite group G , we write acd( G ) to denote the average of the degrees of the irreducible characters of G . We show that if acd( G ) ≤ 3, then G is solvable. Also, if acd( G ) < 3/2, then G is supersolvable, and if acd( G ) < 4/3, then G is nilpotent.
ISSN:	0021-2172 1565-8511
DOI:	10.1007/s11856-013-0013-z