For a characterχof a finite group G,the number cod(χ) := ∣G:ker(χ)∣/χ(1)is called the codegree ofχ.In this paper,we give a solvability criterion for a finite group G depending on the minimum of the ratioχ(1)^(...For a characterχof a finite group G,the number cod(χ) := ∣G:ker(χ)∣/χ(1)is called the codegree ofχ.In this paper,we give a solvability criterion for a finite group G depending on the minimum of the ratioχ(1)^(2)/cod(χ),whenχvaries among the irreducible characters of G.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11971391,12071376,12301018,12171058,12326356)the Natural Science Foundation of Jiangsu Province(Grant No.BK20231356)+1 种基金the Natural Science Foundation for the Universities in Jiangsu Province(Grant No.23KJB110002)The first and second authors are supported by the Chinese Scholarship Council。
文摘For a characterχof a finite group G,the number cod(χ) := ∣G:ker(χ)∣/χ(1)is called the codegree ofχ.In this paper,we give a solvability criterion for a finite group G depending on the minimum of the ratioχ(1)^(2)/cod(χ),whenχvaries among the irreducible characters of G.
