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Retrieving information about a group from its character degrees or from its class sizes |
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| Authors: | Sandro Mattarei |
| Institution: | Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, I-38050 Povo (Trento), Italy |
| 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. |
| Keywords: | Character degrees conjugacy class sizes |
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