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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
Software:
GAP; CHEVIE
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References:
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