On the Connectivity of the Sylow Graph of a Finite Group

Details On the Connectivity of the Sylow Graph of a Finite Group On the Connectivity of the Sylow Graph of a Finite Group

2010-02-25

arxiv.org/abs/1002.4853v4

Mathematics

Combinatorics

8 pp. with Appendix; Fundamental revisions have been done

Scientific paper

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 $\Gamma(G)$.

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