Displaying similar documents to “Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)”

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

Leonid A. Kurdachenko, Howard Smith (2005)

Commentationes Mathematicae Universitatis Carolinae

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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.

Groups with all subgroups permutable or of finite rank

Martyn Dixon, Yalcin Karatas (2012)

Open Mathematics

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In this paper we investigate the structure of X-groups in which every subgroup is permutable or of finite rank. We show that every subgroup of such a group is permutable.

The nilpotency of some groups with all subgroups subnormal.

Leonid A. Kurdachenko, Howard Smith (1998)

Publicacions Matemàtiques

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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.