On Finite Non-Solvable Groups Whose Gruenberg-Kegel Graphs are Isomorphic to the Paw  

作　　者：A.S.Kondrat’ev N.A.Minigulov 

机构地区：[1]N.N.Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences,16 S.Kovalevskaya Str,Yekaterinburg 620108,Russia

出　　处：《Communications in Mathematics and Statistics》2022年第4期653-667,共15页数学与统计通讯（英文）

基　　金：supported by the Russian Science Foundation(project 19-71-10067).

摘　　要：The Gruenberg-Kegel graph(or the prime graph)Γ(G)of a finite group G is a graph,in which the vertex set is the set of all prime divisors of the order of G and two different vertices p and q are adjacent if and only if there exists an element of order pq in G.The paw is a graph on four vertices whose degrees are 1,2,2,3.We consider the problem of describing finite groups whose Gruenberg-Kegel graphs are isomorphic as abstract graphs to the paw.For example,the Gruenberg-Kegel graph of the alternating group A_(10)of degree 10 is isomorphic as abstract graph to the paw.In this paper,we describe finite non-solvable groups G whose Gruenberg-Kegel graphs are isomorphic as abstract graphs to the paw in the case when G has no elements of order 6 or the vertex of degree 1 ofΓ(G)divides the order of the solvable radical of G.

关 键 词：Finite group Non-solvable group Gruenberg-Kegel graph The paw 

分 类 号：O15[理学—数学]