Displaying similar documents to “Locally soluble-by-finite groups with small deviation for non-subnormal subgroups”

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 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...