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G. Cutolo and H. Smith
Locally finite groups with all subgroups subnormal or nilpotent-by-Chernikov
Centr. Eur. J. Math., 10, (2012), pp. 942–949.
doi: 10.2478/s11533-012-0020-z
MathSciNet Zentralblatt Abstract Full Text
Abstract
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.
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