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.
Mattarei, S. (2006). Retrieving information about a group from its character degrees or from its class sizes. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134(8), 2189-2195 [10.1090/S0002-9939-06-08274-8].
Retrieving information about a group from its character degrees or from its class sizes
Mattarei, S
2006
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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