1 Introduction  
2 Local nilpotence of (strong) sandwich groups and strong left 3-Engel elements  
3 Left 3-Engel involutions  
4 Global nilpotence question for \(\langle a\rangle^{G}\) in locally finite 2-groups  
5 Global nilpotence question for \(\langle x\rangle^{G}\) in locally finite \(p\)-groups, for odd \(p\)