On the Connectivity of the Sylow Graph of a Finite Group

DOI10.4236/APM.2012.26058arXiv1002.4853MaRDI QIDQ6217790

Francesco G. Russo

Publication date: 25 February 2010

Abstract: The Sylow graph $Gamma(G)$ of a finite group $G$ originated from recent investigations on the so--called $mathbfN$--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 $mathbfN$--closed classes of groups. The second result deals with a computational criterion, related to the connectivity of $Gamma(G)$.

Mathematics Subject Classification ID

Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Simple groups (20E32) Formations of groups, Fitting classes (20F17)

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