A characterization of finite groups in terms of the codegrees of their characters
Heng Lv, Dongfang Yang, Guohua Qian Β· Journal of Group Theory Β· 2022
Abstract For a character π of a finite group πΊ, the number cod ( Ο ) := | G : ker Ο | / Ο ( 1 ) \operatorname{cod}(\chi):=\lvert G:\operatorname{ker}\chi\rvert/\chi(1) is called the codegree of π. The object of this paper is to classify the finite groups πΊ which have exactly one irreducible character π such that Ο β’ ( 1 ) β€ cod β‘ ( Ο ) \chi(1) mid\operatorname{cod}(\chi) .