Retrieving information about a group from its character degrees or from its class sizes
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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.References
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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
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2189-2195
- MSC (2000): Primary 20C05; Secondary 20C15, 20E45
- DOI: https://doi.org/10.1090/S0002-9939-06-08274-8
- MathSciNet review: 2213690