Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov
Let G be a locally finite group satisfying the condition given in the title and suppose that G is not nilpotent-by-Chernikov. It is shown that G has a section S that is not nilpotent-by-Chernikov, where S is either a p-group or a semi-direct product of the additive group A of a locally finite field F by a subgroup K of the multiplicative group of F, where K acts by multiplication on A and generates F as a ring. Non-(nilpotent-by-Chernikov) extensions of this latter kind exist and are described in detail.
Central European Journal of Mathematics
Cutolo, Giovanni and Smith, Howard. "Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov." Central European Journal of Mathematics (2012) : 942-949.