Character degree graphs and normal subgroups

Author:
I. M. Isaacs

Journal:
Trans. Amer. Math. Soc. **356** (2004), 1155-1183

MSC (2000):
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9947-03-03462-7

Published electronically:
October 6, 2003

MathSciNet review:
2021616

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Abstract | References | Similar Articles | Additional Information

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 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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Additional Information

**I. M. Isaacs**

Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Dr., Madison Wisconsin 53706

Email:
isaacs@math.wisc.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03462-7

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