An answer to a question of Isaacs on character degree graphs |
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Authors: | Alexander Moretó |
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Institution: | Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, Spain |
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Abstract: | Let N be a normal subgroup of a finite group G. We consider the graph Γ(G|N) whose vertices are the prime divisors of the degrees of the irreducible characters of G whose kernel does not contain N and two vertices are joined by an edge if the product of the two primes divides the degree of some of the characters of G whose kernel does not contain N. We prove that if Γ(G|N) is disconnected then G/N is solvable. This proves a strong form of a conjecture of Isaacs. |
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Keywords: | primary 20C15 |
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