Retrieving information about a group from its character degrees or its class sizes
Group Theory
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0510306,
title = {Retrieving information about a group from its character degrees or its class sizes},
author = {Sandro Mattarei},
journal= {arXiv preprint arXiv:math/0510306},
year = {2007}
}
Comments
9 pages, to be published in Proc. Amer. Math. Soc