%0 Journal Article
%T Bounding group orders by large character degrees: A question of Snyder
%A Mark L. Lewis
%J Mathematics
%D 2012
%I arXiv
%R 10.1515/jgt-2014-0011
%X Let $G$ be a nonabelian finite group and let $d$ be an irreducible character degree of $G$. Then there is a positive integer $e$ so that $|G| = d(d+e)$. Snyder has shown that if $e > 1$, then $|G|$ is bounded by a function of $e$. This bound has been improved by Isaacs and by Durfee and Jensen. In this paper, we will show for groups that have a nontrivial, abelian normal subgroup that $|G| \le e^4 - e^3$. We use this to prove that $|G| < e^4 + e^3$ for all groups. Given that there are a number of solvable groups that meet the first bound, it is best possible. Our work makes use of results regarding Camina pairs, Gagola characters, and Suzuki 2-groups.
%U http://arxiv.org/abs/1206.4334v2