论文标题
不可溶解的群体的特征度图具有切割vertex。我
Non-solvable groups whose character degree graph has a cut-vertex. I
论文作者
论文摘要
令G为有限的组。用CD表示G的G（G）一组G的g的程度，我们考虑G的字符度图：这是（简单的无向）图，其顶点是CD（G）中数字的主要分隔线，并且两个不同的顶点P，Q在CD（G）中仅在PQ中均邻接。在从本文开始的三篇论文系列中，我们分析了有限的不可溶解基团的结构，其字符度图具有切割的vertex，即其去除的顶点会增加图形的连接组件的数量。
Let G be a finite group. Denoting by cd(G) the set of degrees of the irreducible complex characters of G, we consider the character degree graph of G: this is the (simple undirected) graph whose vertices are the prime divisors of the numbers in cd(G), and two distinct vertices p, q are adjacent if and only if pq divides some number in cd(G). In the series of three papers starting with the present one, we analyze the structure of the finite non-solvable groups whose character degree graph possesses a cut-vertex, i.e., a vertex whose removal increases the number of connected components of the graph.
