On prime graph components of finite simple groups. (Russian) Zbl 0691.20013

Kondrat’ev, A. S.

Mat. Sb. 180, No. 6, 787-797 (1989).

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

Keywords:

finite groups; prime divisors; orders; graphs

Citations:

Zbl 0471.20013