Retrieving information about a group from its character degrees or its class sizes

Details Retrieving information about a group from its character degrees or its class sizes Retrieving information about a group from its character degrees or its class sizes

2005-10-14

arxiv.org/abs/math/0510306v1

Proc. Amer. Math. Soc. 134 (2006), 2189-2195

Mathematics

Group Theory

9 pages, to be published in Proc. Amer. Math. Soc

Scientific paper

We prove that a 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 a knowledge of the conjugacy class sizes
was known. We prove variations of both results and discuss their similarities.

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