Solvability of finite groups admitting \(S_ 3\) as a fixed-point-free group of operators (Q1084179)

It is an immediate consequence of the famous theorem of Feit and Thompson that a group G which has a group A, isomorphic to the symmetric group of degree 3 acting on it fixed-point-freely so that \((| G|,| A|)=1\), is soluble. The author gives a proof of this result which does not depend on this result. That this is worth achieving is clear from earlier work of \textit{G. Glauberman} [Math. Z. 84, 120-125 (1964; Zbl 0123.026)]. The paper uses the techniques most likely to succeed with skill and inventiveness. He points out that the result has also recently been obtained by B. Dolman in a Ph.D thesis at the University of Adelaide.