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
For an irreducible characterχof a?nite group G,the codegree ofχis de-?ned as|G:ker(χ)|/χ(1).In this paper,the authors determine?nite nonsolvable groups with exactly three nonlinear irreducible character codegrees,...For an irreducible characterχof a?nite group G,the codegree ofχis de-?ned as|G:ker(χ)|/χ(1).In this paper,the authors determine?nite nonsolvable groups with exactly three nonlinear irreducible character codegrees,which are L_(2)(2^(f))for f≥2,PGL_(2)(q)for odd q≥5 or M_(10).展开更多
Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud＇ in their book ＂Characters of Finite Groups＂, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This ...Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud＇ in their book ＂Characters of Finite Groups＂, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind of character graphs of finite groups associated with codegrees. Such graphs have close and obvious connections with character codegree graphs. For example, they have the same number of connected components. By analogy with the work of finite groups whose character graphs （associated with degrees） have no triangles, we conduct a result of classifying finite groups whose character graphs associated with codegrees have no triangles in the latter part of this paper.展开更多
For an irreducible character x of a finite group G,we define its codegree as cod(x)=|G:ker x|/x(1) .In this paper,we introduce some known results x(1)and unsolved problems about character codegrees in finite groups.
Given integer k and a k-graph F,let t(k-1)(n,F)be the minimum integer t such that every k-graph H on n vertices with codegree at least t contains an F-factor.For integers k>3 and 0≤l≤k-1,let y(k,l)be a k-graph wi...Given integer k and a k-graph F,let t(k-1)(n,F)be the minimum integer t such that every k-graph H on n vertices with codegree at least t contains an F-factor.For integers k>3 and 0≤l≤k-1,let y(k,l)be a k-graph with two edges that shares exactly l vertices.Han and Zhao(J.Combin.Theory Ser.A,(2015))asked the following question:For all k≥3,0≤l≤k-1 and sufficiently large n divisible by 2 k-l,determine the exact value of t_(k-1)(n,y(k,l)).In this paper,we show that t(k-1)(n,y(k,l))=n/(2 k-l)for k>3 and 1≤l≤k-2,combining with two previously known results of R?dl,Rucinski and Szemeredi(J.Combin.Theory Ser.A,(2009))and Gao,Han and Zhao(Combinatorics,Probability and Computing,(2019)),the question of Han and Zhao is solved completely.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.
基金supported by the National Natural Science Foundation of China(Nos.12301018,12171058,12326356)the Natural Science Foundation of Jiangsu Province(No.BK20231356)the Natural Science Foundation for the Universities in Jiangsu Province(No.23KJB110002)。
文摘For an irreducible characterχof a?nite group G,the codegree ofχis de-?ned as|G:ker(χ)|/χ(1).In this paper,the authors determine?nite nonsolvable groups with exactly three nonlinear irreducible character codegrees,which are L_(2)(2^(f))for f≥2,PGL_(2)(q)for odd q≥5 or M_(10).
文摘Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud＇ in their book ＂Characters of Finite Groups＂, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind of character graphs of finite groups associated with codegrees. Such graphs have close and obvious connections with character codegree graphs. For example, they have the same number of connected components. By analogy with the work of finite groups whose character graphs （associated with degrees） have no triangles, we conduct a result of classifying finite groups whose character graphs associated with codegrees have no triangles in the latter part of this paper.
基金support provided by the National Natural Science Foundation of China(Grant No.12171058).
文摘For an irreducible character x of a finite group G,we define its codegree as cod(x)=|G:ker x|/x(1) .In this paper,we introduce some known results x(1)and unsolved problems about character codegrees in finite groups.
基金Supported by NNSF of China(Grant No.11671376)NSF of Anhui Province(Grant No.1708085MA18)Anhui Initiative in Quantum Information Technologies(AHY150200)
文摘Given integer k and a k-graph F,let t(k-1)(n,F)be the minimum integer t such that every k-graph H on n vertices with codegree at least t contains an F-factor.For integers k>3 and 0≤l≤k-1,let y(k,l)be a k-graph with two edges that shares exactly l vertices.Han and Zhao(J.Combin.Theory Ser.A,(2015))asked the following question:For all k≥3,0≤l≤k-1 and sufficiently large n divisible by 2 k-l,determine the exact value of t_(k-1)(n,y(k,l)).In this paper,we show that t(k-1)(n,y(k,l))=n/(2 k-l)for k>3 and 1≤l≤k-2,combining with two previously known results of R?dl,Rucinski and Szemeredi(J.Combin.Theory Ser.A,(2009))and Gao,Han and Zhao(Combinatorics,Probability and Computing,(2019)),the question of Han and Zhao is solved completely.
