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Character degree graphs that are complete graphs
Author(s):
Mariagrazia
Bianchi;
David
Chillag;
Mark
L.
Lewis;
Emanuele
Pacifici
Journal:
Proc. Amer. Math. Soc.
135
(2007),
671-676.
MSC (2000):
Primary 20C15;
Secondary 05C25
Posted:
August 31, 2006
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Abstract:
Let  be a finite group, and write  for the set of degrees of irreducible characters of  . We define  to be the graph whose vertex set is  , and there is an edge between  and  if  . We prove that if  is a complete graph, then  is a solvable group.
References:
-
- 1.
- J. H. CONWAY, R. T. CURTIS, S. P. NORTON, R. A. PARKER, AND R. A. WILSON, ``Atlas of Finite Groups,'' Oxford University Press, London, 1984. MR 0827219 (88g:20025)
- 2.
- Y. BERKOVICH, Finite groups with small sums of degrees of some non-linear irreducible characters, J. Algebra 171 (1995), 426-443. MR 1315905 (96c:20015)
- 3.
- R. W. CARTER ``Finite Groups of Lie Type,'' Wiley, New York, 1985. MR 0794307 (87d:20060)
- 4.
- B. HUPPERT, ``Character Theory of Finite Groups,'' Walter DeGruyter, Berlin, 1998. MR 1645304 (99j:20011)
- 5.
- I. M. ISAACS, ``Character Theory of Finite Groups,'' Academic Press, San Diego, 1976. MR 0460423 (57:417)
- 6.
- I. M. ISAACS, Character correspondences in solvable groups, Adv. in Math. 43 (1982), 284-306. MR 0648802 (83i:20007)
- 7.
- M. L. LEWIS, A. MORETÓ, AND T. R. WOLF, Non-divisibility among character degrees, J. Group Theory 8 (2005), 561-588. MR 2165291
- 8.
- M. L. LEWIS, An overview of graphs associated with character degrees and conjugacy class sizes in finite groups, to appear in Rocky Mountain J. Math.
- 9.
- J. K. MCVEY, Bounding graph diameters of nonsolvable groups, J. Algebra 282 (2004), 260-277. MR 2097583 (2005h:20011)
- 10.
- P. SCHMID, Rational matrix groups of a special type, Linear Algebra Appl. 71 (1985), 289-293. MR 0813053 (87e:20018)
- 11.
- P. SCHMID, Extending the Steinberg representation, J. Algebra 150 (1992), 254-256. MR 1174899 (93k:20016)
- 12.
- A. TURULL, Generic fixed point free action of arbitrary finite groups, Math. Z. 187 (1984), 491-503. MR 0760049 (86a:20020)
- 13.
- D. L. WHITE, Degree graphs of simple groups of exceptional Lie type, Comm. Algebra 32 (2004), 3641-3649. MR 2097483 (2005h:20022)
- 14.
- D. L. WHITE, Degree graphs of simple linear and unitary groups, to appear in Comm. Algebra.
- 15.
- D. L. WHITE, Degree graphs of simple orthogonal and symplectic groups, to appear in J. Algebra.
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Additional Information:
Mariagrazia
Bianchi
Affiliation:
Dipartimento di Matematica ``F. Enriques'', Università Degli Studi Di Milano, Via C. Saldini 50, 20133 Milano, Italy
Email:
Mariagrazia.Bianchi@mat.unimi.it
David
Chillag
Affiliation:
Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel
Email:
chillag@techunix.technion.ac.il
Mark
L.
Lewis
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
Email:
lewis@math.kent.edu
Emanuele
Pacifici
Affiliation:
Dipartimento di Matematica ``F. Enriques'', Università Degli Studi Di Milano, Via C. Saldini 50, 20133 Milano, Italy
Email:
Emanuele.Pacifici@mat.unimi.it
DOI:
10.1090/S0002-9939-06-08651-5
PII:
S 0002-9939(06)08651-5
Received by editor(s):
October 4, 2005
Posted:
August 31, 2006
Communicated by:
Jonathan I. Hall
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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