Mathematics – Group Theory
Scientific paper
2011-03-21
Mathematics
Group Theory
12 pages, to appear in Journal of Algebra
Scientific paper
10.1016/j.jalgebra.2010.11.018
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 $\C S_n.$
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