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

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

2005-06-15

arxiv.org/abs/math/0506294v2

Algebra and Logic, v. 44 (2005), N 6, 381-406

Mathematics

Group Theory

Institute of Mathematics, published in "Algebra and Logic", v. 44 (2005), N 6, 381-406

Scientific paper

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.

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