Element orders and character codegrees
Guohua Qian
Abstract
For an irreducible character χ of a finite group G , the codegree of χ is defined by | G : ker χ | / χ ( 1 ) . In this note, we show that if a finite solvable group G has an element of order m , then G admits an irreducible character of codegree divisible by m .
Topics & Concepts
Character (mathematics)MathematicsElement (criminal law)Finite groupOrder (exchange)Group (periodic table)Pure mathematicsCharacter tableCombinatoricsAlgebra over a fieldGeometryLawPhysicsPolitical scienceQuantum mechanicsEconomicsFinanceFinite Group Theory ResearchCoding theory and cryptographygraph theory and CDMA systems