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RESEARCH PRODUCT

An answer to a question of Isaacs on character degree graphs

Alexander Moretó

subject

Normal subgroupCombinatoricsDiscrete mathematicsFinite groupMathematics(all)ConjectureGeneral MathematicsProjective charactersNormal subgroupsSolvable groupsCharacter degreesGraphMathematics

description

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.

yearjournalcountryeditionlanguage
2006-03-01Advances in Mathematics
10.1016/j.aim.2004.11.008http://dx.doi.org/10.1016/j.aim.2004.11.008