On the Connectivity of the Sylow Graph of a Finite Group

Abstract

The Sylow graph $\Gamma (G)$ of a finite group $G$ originated from recent investigations on the so--called $\mathbf{N}$--closed classes of groups. The connectivity of $\Gamma (G)$ 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 $\Gamma (G)$ 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 $\Gamma (G)$.

8 pp. with Appendix; Fundamental revisions have been done

References in corpus (2)

• The probability that $x$ and $y$ commute in a compact group
• Commuting powers and exterior degree of finite groups

Cited by in corpus (1)

• Considerations on the subgroup commutativity degree and related notions