On finite simple groups with the set of element orders as in a Frobenius group or a double Frobenius group.
Using the classification, it is proved that the only finite simple groups having the same element orders as a Frobenius group are \(L_3(3)\) and \(U_3(3)\). Examples of corresponding Frobenius groups are specific groups of shape \(13^2:2S^-_4\) and \(7^4:3:8\), respectively. Similarly, the only possible finite simple groups having the same element orders as a double Frobenius group (a group of shape \(A:B:C\) where \(A:B\) and \(B:C\) are Frobenius groups) are \(U_3(3)\) and \(S_4(3)\). No double Frobenius groups with these sets of element orders are apparently known.
scientific article; zbMATH DE number 2115570