Symmetric groups are determined by their character degrees

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 $G\cong S_n.$ As a consequence, we show that $S_n$ is uniquely determined by the structure of the complex group algebra $\C S_n.$

12 pages, to appear in Journal of Algebra

Cited by in corpus (4)

• Simple classical groups of Lie type are determined by their character degrees
• Complex group algebras of the double covers of the symmetric and alternating groups
• The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups
• Huppert's Conjecture for Alternating groups