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 | 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.

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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:
https://doi.org/10.1090/S0002-9939-06-08274-8

Keywords:
Character degrees,
conjugacy class sizes.

Received by editor(s):
November 26, 2004

Received by editor(s) in revised form:
March 2, 2005

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.