Groups whose subgroups have small automizers
A SANS-group was defined by Brandl and the reviewer to be a group \(G\) such that \(N_G(H)=HC_G(H)\) for every nonabelian subgroup \(H\) of \(G\) and the structure of the finite SANS-groups was completely elucidated in a previous paper. In the paper under review, the authors continue the program, initiated by the reviewer, of describing groups via conditions imposed on the automizers of their subgroups. By carefully finding their way through the maze of finiteness conditions and by fully using the available information from the finite case, the authors manage to describe the locally finite non-nilpotent SANS-groups and the locally soluble non-nilpotent SANS-groups.
scientific article; zbMATH DE number 1279147