Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov
Central European Journal of Mathematics
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.
Cutolo, Giovanni and Smith, Howard. "Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov." Central European Journal of Mathematics 10, no. 3 (2012) : 942-949.