Character degree graphs and normal subgroups

We consider the degrees of those irreducible characters of a group G whose kernels do not contain a given normal subgroup N. We show that if N \subseteq G' and N is not perfect, then the common-divisor graph on this set of integers has at most two connected components. Also, if N is solvable, w...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2004-03, Vol.356 (3), p.1155-1183
Main Author: Isaacs, I. M.
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Counterexamples
Exact sciences and technology
Gin
Group theory
Group theory and generalizations
Homomorphisms
Integers
Mathematical theorems
Mathematics
Prime numbers
Sciences and techniques of general use
Vertices
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Summary:We consider the degrees of those irreducible characters of a group G whose kernels do not contain a given normal subgroup N. We show that if N \subseteq G' and N is not perfect, then the common-divisor graph on this set of integers has at most two connected components. Also, if N is solvable, we obtain bounds on the diameters of the components of this graph and, in the disconnected case, we study the structure of N and of G.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-03-03462-7