The nilpotency of some groups with all subgroups subnormal.

Leonid A. Kurdachenko; Howard Smith

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Displaying similar documents to “The nilpotency of some groups with all subgroups subnormal.”

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...

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Groups with finite conjugacy classes of subnormal subgroups

Carlo Casolo (1989)

Rendiconti del Seminario Matematico della Università di Padova

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Anti-CC-groups and anti-PC-groups.

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Groups whose all subgroups are ascendant or self-normalizing

Leonid Kurdachenko, Javier Otal, Alessio Russo, Giovanni Vincenzi (2011)

Open Mathematics

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This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups,...

Groups in which the derived groups of all 2-generator subgroups are cyclic

Patrizia Longobardi, Mercede Maj, Howard Smith (2006)

Rendiconti del Seminario Matematico della Università di Padova

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On maximal subgroups of minimax groups

Silvana Franciosi, Francesco de Giovanni (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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It is proved that a soluble residually finite minimax group is finite-by-nilpotent if and only if it has only finitely many maximal subgroups which are not normal.