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)



A solvable group whose character degree graph has diameter $3$

Author: Mark L. Lewis
Journal: Proc. Amer. Math. Soc. 130 (2002), 625-630
MSC (2000): Primary 20C15
Published electronically: June 20, 2001
MathSciNet review: 1866010
Full-text PDF

Abstract | References | Similar Articles | Additional Information


We show that there is a solvable group $G$ so that the character degree graph of $G$ has diameter $3$.

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

  • 1. A. Hanaki, A condition on lengths of conjugacy classes and character degrees, Osaka J. Math. 33 (1996), 207-216. MR 97b:20007
  • 2. B. Huppert, Research in representation theory at Mainz (1984-1990), Progr. Math. 95 (1991), 17-36. MR 92c:20011
  • 3. B. Huppert, Character Theory of Finite Groups, deGruyter Expositions in Mathematics 25, Berlin, 1998. MR 99j:20011
  • 4. I. M. Isaacs, Character Theory of Finite Groups, Academic Press, New York, 1976. MR 57:417
  • 5. I. M. Isaacs, Coprime group actions fixing all nonlinear irreducible characters, Can. J. Math. 41 (1989), 68-82. MR 90j:20038
  • 6. I. M. Isaacs and G. Knutson, Irreducible character degrees and normal subgroups, J. Algebra 199 (1998), 302-326. MR 98m:20013
  • 7. M. L. Lewis, Solvable groups with degree graphs having 5 vertices and diameter 3, Preprint.
  • 8. O. Manz, W. Willems, and T. R. Wolf, The diameter of the character degree graph, J. Reine Angew. Math. 402 (1989), 181-198. MR 90i:20007
  • 9. O. Manz and T. R. Wolf, Representations of Solvable Groups, Cambridge University Press, Cambridge, 1993. MR 95c:20013
  • 10. P. P. Pálfy, On the character degree graph of solvable groups, I, Period. Math. Hungar. 36 (1998), 61-65. MR 2000c:20019
  • 11. J. M. Riedl, Character degrees, class sizes, and normal subgroups of a certain class of $p$-groups, J. Algebra 218 (1999), 190-215. MR 2000f:20025
  • 12. J. Zhang, On a problem by Huppert, Acta Scientiarum Naturalium Universitatis Pekinensis 34 (1998), 143-150. MR 99j:20014

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20C15

Retrieve articles in all journals with MSC (2000): 20C15

Additional Information

Mark L. Lewis
Affiliation: Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242

Received by editor(s): May 19, 2000
Received by editor(s) in revised form: August 23, 2000
Published electronically: June 20, 2001
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society