On the Connectivity of the Sylow Graph of a Finite Group

Abstract

The Sylow graph $Γ(G)$ of a finite group $G$ originated from recent investigations on the so--called $\mathbf{N}$--closed classes of groups. The connectivity of $Γ(G)$ was proved only few years ago, involving the classification of finite simple groups, and the structure of $G$ may be strongly restricted, once information on $Γ(G)$ are given. The first result of the present paper deals with a condition on $\mathbf{N}$--closed classes of groups. The second result deals with a computational criterion, related to the connectivity of $Γ(G)$.