%0 Journal Article
%T Symmetric groups are determined by their character degrees
%A H. P. Tong-Viet
%J Mathematics
%D 2011
%I arXiv
%R 10.1016/j.jalgebra.2010.11.018
%X 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 $G\cong S_n.$ As a consequence, we show that $S_n$ is uniquely determined by the structure of the complex group algebra $\C S_n.$
%U http://arxiv.org/abs/1103.3939v1