Verifying Huppert's conjecture for \(^2G_2(q^2)\).
Let \(\text{cd}(G)\) denote the set of character degrees of a finite group \(G\). Then Huppert's conjecture states that if \(H\) is a finite group with \(\text{cd}(G)=\text{cd}(H)\), then \(G\) is isomorphic to the direct product of \(H\) by a group \(A\), where \(A\) is an Abelian group. This conjecture is proved for the Suzuki groups and a few of simple groups of Lie type and some other simple groups by \textit{B. Huppert} [in Ill. J. Math. 44, No. 4, 828-842 (2000; Zbl 0972.20006)]. In the paper under review the author proves the conjecture for the twisted Ree group \(^2G_2(q^2)\) for \(q^2=3^{2m+1}\), \(m\) greater or equal to \(1\).
scientific article; zbMATH DE number 6054169
scientific article