Infinite groups with many generalized normal subgroups

Abstract

A subgroup $X$ of a group $G$ is almost normal if the index $|G:N_G(X)|$ is finite‎, ‎while $X$ is nearly normal if it has finite index in the normal closure $X^G$‎. ‎This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal‎.