An Adjacency Criterion for the Prime Graph of a Finite Simple Group
For every finite non-Abelian simple group, we give an exhaustive arithmetic criterion for adjacency of vertices in a prime graph of the group. For the prime graph of every finite simple group, this criterion is used to determine an independent set with a maximal number of vertices and an independent set with a maximal number of vertices containing 2, and to define orders on these sets; the information obtained is collected in tables. We consider several applications of these results to various problems in finite group theory, in particular, to the recognition-by-spectra problem for finite groups.
Keywordsfinite group finite simple group group of Lie type spectrum of a finite group recognition by spectrum prime graph of a finite group independence number of a prime graph 2-independence number of a prime graph
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