An adjacency criterion for the prime graph of a finite simple group

In the paper we give an exhaustive arithmetic criterion of adjacency in prime graph \(GK(G)\) for every finite nonabelian simple group \(G\). By using this criterion for all finite simple groups an independence set with the maximal number of vertices, an independence set containing 2 with the maxima...

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Bibliographic Details
Published in:arXiv.org 2010-07
Main Authors: Vasilév, Anrei V, Vdovin, Evgeny P
Format: Article
Language:English
Subjects:
Apexes
Criteria
Group theory
Online Access:Get full text
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Summary:In the paper we give an exhaustive arithmetic criterion of adjacency in prime graph \(GK(G)\) for every finite nonabelian simple group \(G\). By using this criterion for all finite simple groups an independence set with the maximal number of vertices, an independence set containing 2 with the maximal number of vertices, and the orders of these independence sets are given. We assemble this information in the tables at the end of the paper. Several applications of obtained results for various problems of finite group theory are considered.
ISSN:2331-8422
DOI:10.48550/arxiv.0506294