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...