Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

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

Author(s): Mark L. Lewis
Journal: Proc. Amer. Math. Soc. 130 (2002), 625-630.
MSC (2000): Primary 20C15
Posted: June 20, 2001
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

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


References:

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
Email: lewis@mcs.kent.edu

DOI: 10.1090/S0002-9939-01-06091-9
PII: S 0002-9939(01)06091-9
Received by editor(s): May 19, 2000
Received by editor(s) in revised form: August 23, 2000
Posted: June 20, 2001
Communicated by: Stephen D. Smith
Copyright of article: Copyright 2001, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google