Nilpotence in finitary linear groups
A finitary linear group is a group \(G\) of automorphisms of a vector space of infinite dimension over a field such that every element \(g \in G\) fixes elementwise a subspace of finite codimension. The paper under review studies radicals of \(G\) related to the locally nilpotent one. The author considers 13 types of radicals and analyzes which of them coincide in the class of finitary linear groups. A typical result shows that the locally nilpotent radical coincides with the Gruenberg radical constituted by the set of elements \(g \in G\) such that \(\langle g\rangle\) is a member of a finite ascending series of subnormal subgroups.
scientific article; zbMATH DE number 614379