The Character Degree Graph with Fifth-order Circles
Zhang Guang-xiang · Neimenggu Shi-da xuebao. Zhexue shehui kexue hanwen ban · 2013
A character degree graph Δ has bounded Fitting height if there is a bound on the Fitting height for the solvable group G with Δ(G)=Δ.Thus we can have a conjecture that if G is a solvable group where Δ(G) is a graph with bounded Fitting height,then G has Fitting height at most 4.It has been proved in some paper that the conjecture is right at least in the two situations.The aforementioned methods and conclusions are exploited in this paper,the authors prove that the Fitting height of a finite solvable group that has a character degree graph with fifth-order circles is at most 4;and they also discuss on the property of a kind of character degree graph with fifth-order circles.