Cyclic quasinormal subgroups of arbitrary groups

In recent years several papers have appeared showing how cyclic quasinormal subgroups are embedded in finite groups and many structure theorems have been proved. The purpose of the present work is twofold. First we show that, without exception, all of these theorems remain valid for finite cyclic quasinormal subgroups of infinite groups. Secondly we obtain analogous results for infinite cyclic quasinormal subgroups, where the statements turn out to be even stronger.