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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0020-z,
author = {Giovanni Cutolo and Howard Smith},
title = {Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {942-949},
zbl = {1257.20039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0020-z}
}
Giovanni Cutolo; Howard Smith. Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov. Open Mathematics, Tome 10 (2012) pp. 942-949. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0020-z/
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