Classical groups as Frobenius complement

Abstract

The Frobenius group \(G\) belongs to an important class of groups that more than 100 years ago was defined by F. G. Frobenius who proved that \(G\) is a semi-direct product of a normal subgroup \(K\) of \(G\) called kernel by another non-trivial subgroup \(H\) called the complement. In this case we show that a few of the classical finite groups can be Frobenius complement.