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On the average character degree of finite groups
Author(s) -
Moretó Alexander,
Nguyen Hung Ngoc
Publication year - 2014
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt107
Subject(s) - mathematics , character (mathematics) , conjecture , degree (music) , finite group , combinatorics , group (periodic table) , pure mathematics , solvable group , geometry , abelian group , chemistry , physics , organic chemistry , acoustics
We prove that if the average of the degrees of the irreducible characters of a finite group G is less than 16 5 , then G is solvable. This solves a conjecture of I. M. Isaacs, M. Loukaki and the first author. We discuss related questions.