In this paper, we construct a new class of finite groups whose common divisor graphs are complete graphs, while there is no prime dividing all the nontrivial degrees.
In this article, we prove that a finite solvable group with character degree graph containing at least four vertices has Fitting height at most 4 if each derived subgraph of four vertices has total degree not more tha...In this article, we prove that a finite solvable group with character degree graph containing at least four vertices has Fitting height at most 4 if each derived subgraph of four vertices has total degree not more than 8. We also prove that if the vertex set ρ（G） of the character degree graph △（G） of a solvable group G is a disjoint union ρ（G） =π1∪π2, where ｜πi｜≥2 and pi,qi∈πi for i = 1,2, and no vertex in πl is adjacent in △（G） to any vertex in π2 except for p1p2 and q1q2, then the Fitting height of G is at most 4.展开更多
基金Supported by Science Foundation of He’nan University of Technology(Grant Nos.2011BS043 and 2010BS048)Tianyuan Fund of Mathematics of China(Grant No.11226046)
文摘In this paper, we construct a new class of finite groups whose common divisor graphs are complete graphs, while there is no prime dividing all the nontrivial degrees.
文摘In this article, we prove that a finite solvable group with character degree graph containing at least four vertices has Fitting height at most 4 if each derived subgraph of four vertices has total degree not more than 8. We also prove that if the vertex set ρ（G） of the character degree graph △（G） of a solvable group G is a disjoint union ρ（G） =π1∪π2, where ｜πi｜≥2 and pi,qi∈πi for i = 1,2, and no vertex in πl is adjacent in △（G） to any vertex in π2 except for p1p2 and q1q2, then the Fitting height of G is at most 4.
