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Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov

100%

Cutolo G., Smith H.

Open Mathematics

2012

tom 10

nr 3

942-949

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.

On locally graded barely transitive groups

100%

Betin C., Kuzucuoğlu M.

Open Mathematics

2013

tom 11

nr 7

1188-1196

We show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.

Ograniczanie wyników

2 Open Mathematics

1 Betin C.

1 Cutolo G.

1 Kuzucuoğlu M.

1 Smith H.

1 2013

1 2012

Wyniki wyszukiwania

Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov

On locally graded barely transitive groups