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.
Locally finite groups with all subgroups subnormal or nilpotent-by-Chernikov / Cutolo, Giovanni; H., Smith. - In: CENTRAL EUROPEAN JOURNAL OF MATHEMATICS. - ISSN 1644-3616. - 10:3(2012), pp. 942-949. [10.2478/s11533-012-0020-z]
Locally finite groups with all subgroups subnormal or nilpotent-by-Chernikov
CUTOLO, GIOVANNI;
2012
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.