Currently displaying 1 – 18 of 18

Showing per page

Order by Relevance | Title | Year of publication

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

Giovanni CutoloHoward Smith — 2012

Open Mathematics

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...

Groups with small deviation for non-subnormal subgroups

Leonid KurdachenkoHoward Smith — 2009

Open Mathematics

We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent,...

The nilpotency of some groups with all subgroups subnormal.

Leonid A. KurdachenkoHoward Smith — 1998

Publicacions Matemàtiques

Let G be a group with all subgroups subnormal. A normal subgroup N of G is said to be G-minimax if it has a finite G-invariant series whose factors are abelian and satisfy either max-G or min- G. It is proved that if the normal closure of every element of G is G-minimax then G is nilpotent and the normal closure of every element is minimax. Further results of this type are also obtained.

Groups with the weak minimal condition for non-subnormal subgroups II

Leonid A. KurdachenkoHoward Smith — 2005

Commentationes Mathematicae Universitatis Carolinae

Let G be a group with the property that there are no infinite descending chains of non-subnormal subgroups of G for which all successive indices are infinite. The main result is that if G is a locally (soluble-by-finite) group with this property then either G has subgroups subnormal or G is a soluble-by-finite minimax group. This result fills a gap left in an earlier paper by the same authors on groups with the stated property.

Locally soluble-by-finite groups with small deviation for non-subnormal subgroups

Leonid A. KurdachenkoHoward Smith — 2007

Commentationes Mathematicae Universitatis Carolinae

A group G has subnormal deviation at most 1 if, for every descending chain H 0 > H 1 > of non-subnormal subgroups of G , for all but finitely many i there is no infinite descending chain of non-subnormal subgroups of G that contain H i + 1 and are contained in H i . This property 𝔓 , say, was investigated in a previous paper by the authors, where soluble groups with 𝔓 and locally nilpotent groups with 𝔓 were effectively classified. The present article affirms a conjecture from that article by showing that locally soluble-by-finite...

Page 1

Download Results (CSV)