Transactions of the American Mathematical Society

Author(s): I. M. Isaacs
Journal: Trans. Amer. Math. Soc. 356 (2004), 1155-1183.
MSC (2000): Primary 20C15
Posted: October 6, 2003
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Abstract: We consider the degrees of those irreducible characters of a group

whose kernels do not contain a given normal subgroup

. We show that if $N \subseteq G'$ and

is not perfect, then the common-divisor graph on this set of integers has at most two connected components. Also, if

is solvable, we obtain bounds on the diameters of the components of this graph and, in the disconnected case, we study the structure of

and of

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

DOI: 10.1090/S0002-9947-03-03462-7
PII: S 0002-9947(03)03462-7
Received by editor(s): November 6, 2002
Posted: October 6, 2003
Additional Notes: This research was partially supported by a grant from the U. S. National Security Agency
Copyright of article: Copyright 2003, American Mathematical Society

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