Retrieving information about a group from its character degrees or from its class sizes
Authors:
Sandro Mattarei
Affiliation:
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.