Groups with finite conjugacy classes of subnormal subgroups
Carlo Casolo (1989)
Rendiconti del Seminario Matematico della Università di Padova
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Carlo Casolo (1989)
Rendiconti del Seminario Matematico della Università di Padova
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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...
Stewart E. Stonehewer, Giovanni Zacher (2004)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Let be any group and let be an abelian quasinormal subgroup of . If is any positive integer, either odd or divisible by , then we prove that the subgroup is also quasinormal in .
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 is called a generalized radical, if 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 be a locally generalized...
Simion Breaz, Grigore Călugăreanu (2002)
Commentationes Mathematicae Universitatis Carolinae
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The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.