On prime graph components of finite simple groups. (Russian) Zbl 0691.20013
Let \(G\) be a finite group and \(\pi(G)\) be the set of all prime divisors of the order of \(G\). Let \(\Gamma(G)\) be the graph with the vertex set \(\pi(G)\) in which \((p,q)\) is an edge if and only if \(G\) has an element of order \(pq\). The author finishes the classification of groups \(G\) for which \(\Gamma(G)\) is disconnected. The investigation of such groups was started by K. Gruenberg and O. H. Kegel and continued by J. S. Williams [J. Algebra 69, 487-513 (1981; Zbl 0471.20013)].
Reviewer: V.Mazurov
MSC:
| 20D05 | Finite simple groups and their classification |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
