Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov |
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Authors: | Giovanni Cutolo Howard Smith |
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Institution: | 1.Dipartimento di Matematica e Applicazioni “R. Caccioppoli”,Università degli Studi di Napoli “Federico II”,Napoli,Italy;2.Department of Mathematics,Bucknell University,Lewisburg,USA |
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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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