[For the entire collection see Zbl 0695.00013.]
Let L be a field, G a finite subgroup of Aut L and \(L_ G\) the subfield of elements fixed by G. The action of the group ring \(L_ GG\) on L is described by \[ X^{\sum_{\gamma \in G}C_{\gamma}\gamma}:=\sum_{\gamma \in G}C_{\gamma}X^{\gamma},\quad C_{\gamma}\in L_ G,\quad X\in L. \] Let \(Stab_{Aut G}G\) be the set of all \(\sigma\in Aut L\) such that \(X^{\sigma}=X\) for all \(L_ GG\)-submodules X of L. The main result of the paper is the following: Let \(p:=char L\), \(Stab_{Aut L}G\neq G\). If \(p\neq 0\) then G is abelian and the Sylow p-subgroup of G is cyclic. If \(p=0\) then G is a subdirect product of metacyclic groups, in particular G is metabelian and supersoluble. The author says that an example of a field L and a finite nonabelian subgroup G of Aut L with G \(\neq Stab_{Aut L}G\) is not known to him.