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Degree graphs of simple groups. (English) Zbl 1180.20008
Let $$G$$ be a finite group, and let $$\text{cd}(G)$$ be the set of irreducible character degrees of $$G$$. The degree graph $$\Delta(G)$$ is the graph whose set of vertices is the set of primes that divide degrees in $$\text{cd}(G)$$, with an edge between $$p$$ and $$q$$ if $$pq$$ divides $$a$$ for some degree $$a\in\text{cd}(G)$$.
In this paper, the author gives a survey in which the degree graphs for all nonabelian finite simple groups are described.

##### MSC:
 20C33 Representations of finite groups of Lie type 20C34 Representations of sporadic groups 20C15 Ordinary representations and characters 20D06 Simple groups: alternating groups and groups of Lie type 20D08 Simple groups: sporadic groups 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 20D60 Arithmetic and combinatorial problems involving abstract finite groups
GAP; CHEVIE
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