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Groups with small deviation for non-subnormal subgroups

Leonid Kurdachenko, Howard Smith (2009)

Open Mathematics

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 most 1 is nilpotent,...

Groups with soluble factor groups and projectivities

Giorgio Busetto, Federico Menegazzo (1985)

Rendiconti del Seminario Matematico della Università di Padova

Groups with subnormal subgroups of bounded defect

Carlo Casolo (1987)

Rendiconti del Seminario Matematico della Università di Padova

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

Leonid A. Kurdachenko, Howard 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 all 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.