Groups with normality conditions for subgroups of infinite rank. (Q400696)

A recent theme in infinite group theory is to study groups whose subgroups of infinite rank satisfy some additional property, which is then used to see how this affects the structure of the entire group. This theme is once again taken up very nicely in this paper.NEWLINENEWLINE The authors obtain three main results connected to the properties ``almost normal'', ``nearly normal'', and ``normal-by-finite``. The following result (Theorem B) is typical of the kind obtained: Let \(G\) be a generalized radical group of infinite rank in which every subgroup of infinite rank is nearly normal. Then the commutator subgroup of \(G\) is finite.