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Retrieving information about a group from its character degrees or from its class sizes
Author:
Sandro Mattarei
Journal:
Proc. Amer. Math. Soc. 134 (2006), 2189-2195
MSC (2000):
Primary 20C05; Secondary 20C15, 20E45
Posted:
February 2, 2006
MathSciNet review:
2213690
Full-text PDF Free Access
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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
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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)
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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:
http://dx.doi.org/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
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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