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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Character degree graphs and normal subgroups


Author: I. M. Isaacs
Journal: Trans. Amer. Math. Soc. 356 (2004), 1155-1183
MSC (2000): Primary 20C15
Published electronically: October 6, 2003
MathSciNet review: 2021616
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Abstract: 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 $G$.


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Additional Information

I. M. Isaacs
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Dr., Madison Wisconsin 53706
Email: isaacs@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03462-7
PII: S 0002-9947(03)03462-7
Received by editor(s): November 6, 2002
Published electronically: October 6, 2003
Additional Notes: This research was partially supported by a grant from the U. S. National Security Agency
Article copyright: © Copyright 2003 American Mathematical Society