# An Adjacency Criterion for the Prime Graph of a Finite Simple Group

- Authors
- Type
- Published Article
- Journal
- Algebra and Logic
- Publisher
- Kluwer Academic Publishers-Consultants Bureau
- Publication Date
- Nov 01, 2005
- Volume
- 44
- Issue
- 6
- Pages
- 381–406
- Identifiers
- DOI: 10.1007/s10469-005-0037-5
- Source
- Springer Nature
- Keywords
- License
- Yellow

## Abstract

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.