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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...

On some properties of the upper central series in Leibniz algebras

Leonid A. KurdachenkoJavier OtalIgor Ya. Subbotin — 2019

Commentationes Mathematicae Universitatis Carolinae

This article discusses the Leibniz algebras whose upper hypercenter has finite codimension. It is proved that such an algebra L includes a finite dimensional ideal K such that the factor-algebra L / K is hypercentral. This result is an extension to the Leibniz algebra of the corresponding result obtained earlier for Lie algebras. It is also analogous to the corresponding results obtained for groups and modules.

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