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A curiosity concerning the degrees of the characters of a finite group

A curiosity concerning the degrees of the characters of a finite group

Let <italic>G</italic> be a finite group with irreducible characters <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartSet ellipsis comma chi comma ellipsis EndSet"> <mml:semantics> <mml:mrow> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mo>…<!-- … --></mml:mo> <mml:mo>,</mml:mo> <mml:mi>χ<!-- χ --></mml:mi> <mml:mo>,</mml:mo> <mml:mo>…<!-- … --></mml:mo> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\{ \ldots ,\chi , \ldots \}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> …