Symmetric groups are determined by their character degrees

H. P. Tong-Viet

doi:10.1016/j.jalgebra.2010.11.018

paper

Symmetric groups are determined by their character degrees

arXiv:1103.3939 · doi:10.1016/j.jalgebra.2010.11.018

Abstract

Let $G$ be a finite group. Let $X_{1} (G)$ be the first column of the ordinary character table of $G .$ In this paper, we will show that if $X_{1} (G) = X_{1} (S_{n}),$ then $G ≅ S_{n} .$ As a consequence, we show that $S_{n}$ is uniquely determined by the structure of the complex group algebra $\C S_n.$

12 pages, to appear in Journal of Algebra