Displaying similar documents to “Groups with the weak minimal condition for non-subnormal subgroups II”

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

Leonid A. Kurdachenko, Howard Smith (2007)

Commentationes Mathematicae Universitatis Carolinae

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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...

Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)

Abdelhafid Badis, Nadir Trabelsi (2011)

Open Mathematics

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Our main result is that a locally graded group whose proper subgroups are Baer-by-Chernikov is itself Baer-by-Chernikov. We prove also that a locally (soluble-by-finite) group whose proper subgroups are Baer-by-(finite rank) is itself Baer-by-(finite rank) if either it is locally of finite rank but not locally finite or it has no infinite simple images.

Groups with small deviation for non-subnormal subgroups

Leonid Kurdachenko, Howard Smith (2009)

Open Mathematics

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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...

On non-periodic groups whose finitely generated subgroups are either permutable or pronormal

L. A. Kurdachenko, I. Ya. Subbotin, T. I. Ermolkevich (2013)

Mathematica Bohemica

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The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group G is called a generalized radical, if G has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the followingTheorem. Let G be a locally generalized...