A solvable group whose character degree graph has diameter

Author:
Mark L. Lewis

Journal:
Proc. Amer. Math. Soc. **130** (2002), 625-630

MSC (2000):
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9939-01-06091-9

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 so that the character degree graph of has diameter .

**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 -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**

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

Email:
lewis@mcs.kent.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-06091-9

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