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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
Published electronically: February 2, 2006
MathSciNet review: 2213690
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Abstract: We prove that knowledge of the character degrees of a finite group $ G$ and of their multiplicities determines whether $ G$ has a Sylow $ p$-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.

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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

Keywords: Character degrees, conjugacy class sizes.
Received by editor(s): November 26, 2004
Received by editor(s) in revised form: March 2, 2005
Published electronically: 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 28 years after publication.

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