Some examples on lifting the commutant of a subnormal operator

M. B. Abrahamse

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A note on subnormal operators

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Subnormal composition factors of infinite groups

Stewart E. Stonehewer (1980)

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Wielandt series and defects of subnormal subgroups in finite soluble groups

Carlo Casolo (1992)

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Francesco De Giovanni, Alessio Russo (1999)

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On subnormal series with factors of finite rank : the join problem

Howard Smith (1992)

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Groups with all subgroups subnormal or nilpotent-by-Chernikov

Howard Smith (2011)

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Groups with small deviation for non-subnormal subgroups

Leonid Kurdachenko, Howard Smith (2009)

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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...

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 $H_{0} > H_{1} > \dots$ 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...