arXiv subjects

H. P. Tong-Viet

Publications and source records attributed to H. P. Tong-Viet.

2 recordsLinked to original sources

arXiv2011

The Simple Ree groups ${}^2F_4(q^2)$ are determined by the set of their character degrees

Let $G$ be a finite group. Let ${\rm{cd}}(G)$ be the set of all complex irreducible character degrees of $G.$ In this paper, we will show that if ${\rm{cd}}(G)={\rm{cd}}(H),$ where $H$ is the simple Ree group ${}^2F_4(q^2),q^2\geq 8,$ then $G\cong H\times A,$ where $A$ is an abelian group. This verifies Huppert's Conjecture for the simple Ree groups ${}^2F_4(q^2)$ when $q^2\geq 8.$

math.GR↗

arXiv2011

Symmetric groups are determined by their character degrees

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 $\C S_n.$

math.GR↗