Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Coprimeness among irreducible character degrees of finite solvable groups

Author: Diane Benjamin
Journal: Proc. Amer. Math. Soc. 125 (1997), 2831-2837
MSC (1991): Primary 20C15
MathSciNet review: 1443370
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given a finite solvable group $G$, we say that $G$ has property $P_{k}$ if every set of $k$ distinct irreducible character degrees of $G$ is (setwise) relatively prime. Let $k(G)$ be the smallest positive integer such that $G$ satisfies property $P_{k}$. We derive a bound, which is quadratic in $k(G)$, for the total number of irreducible character degrees of $G$. Three exceptional cases occur; examples are constructed which verify the sharpness of the bound in each of these special cases.

References [Enhancements On Off] (What's this?)

  • I. Martin Isaacs, Character theory of finite groups, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure and Applied Mathematics, No. 69. MR 0460423
  • B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
  • I. M. Isaacs and D. S. Passman, A characterization of groups in terms of the degrees of their characters. II, Pacific J. Math. 24 (1968), 467–510. MR 241524
  • Bertram Huppert, Research in representation theory at Mainz (1984–1990), Representation theory of finite groups and finite-dimensional algebras (Bielefeld, 1991) Progr. Math., vol. 95, Birkhäuser, Basel, 1991, pp. 17–36. MR 1112156

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20C15

Retrieve articles in all journals with MSC (1991): 20C15

Additional Information

Diane Benjamin
Affiliation: Department of Mathematics, University of Wisconsin–Platteville, Platteville, Wisconsin 53818

Received by editor(s): April 4, 1996
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society