|
Retrieving information about a group from its character degrees or from its class sizes
Author(s):
Sandro
Mattarei
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2189-2195.
MSC (2000):
Primary 20C05;
Secondary 20C15, 20E45
Posted:
February 2, 2006
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove that knowledge of the character degrees of a finite group  and of their multiplicities determines whether  has a Sylow  -subgroup as a direct factor. An analogous result based on knowledge of the conjugacy class sizes is known. We prove variations of both results and discuss their similarities.
References:
-
- [CH93]
- John Cossey and Trevor Hawkes, Computing the order of the nilpotent residual of a finite group from knowledge of its group algebra, Arch. Math. (Basel) 60 (1993), no. 2, 115-120. MR 1199667 (93m:20006)
- [CHM92]
- John Cossey, Trevor Hawkes, and Avinoam Mann, A criterion for a group to be nilpotent, Bull. London Math. Soc. 24 (1992), no. 3, 267-270. MR 1157262 (93c:20040)
- [Haw94]
- Trevor Hawkes, On groups with isomorphic complex group algebras, J. Algebra 167 (1994), no. 3, 557-577. MR 1287060 (95f:20009)
- [Hup67]
- B. Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin, 1967, Die Grundlehren der Mathematischen Wissenschaften, Band 134. MR 0224703 (37:302)
- [Hup91]
- 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 (92c:20011)
- [Isa86]
- I. M. Isaacs, Recovering information about a group from its complex group algebra, Arch. Math. (Basel) 47 (1986), no. 4, 293-295. MR 0866514 (87m:20017)
- [Isa94]
- I. Martin Isaacs, Character theory of finite groups, Dover Publications Inc., New York, 1994, Corrected reprint of the 1976 original [Academic Press, New York; MR 0460423 (57:417)] MR 1280461
- [Mic86]
- Gerhard O. Michler, A finite simple group of Lie type has
 -blocks with different defects,  , J. Algebra 104 (1986), no. 2, 220-230. MR 0866772 (87m:20038)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
20C05,
20C15, 20E45
Retrieve articles in all Journals with MSC
(2000):
20C05,
20C15, 20E45
Additional Information:
Sandro
Mattarei
Affiliation:
Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, I-38050 Povo (Trento), Italy
Email:
mattarei@science.unitn.it
DOI:
10.1090/S0002-9939-06-08274-8
PII:
S 0002-9939(06)08274-8
Keywords:
Character degrees,
conjugacy class sizes.
Received by editor(s):
November 26, 2004
Received by editor(s) in revised form:
March 2, 2005
Posted:
February 2, 2006
Additional Notes:
The author is grateful to Ministero dell'Istruzione, dell'Università e della Ricerca, Italy, for financial support of the project ``Graded Lie algebras and pro-$p$-groups of finite width''.
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.
|
Comments: webmaster@ams.org