Displaying similar documents to “Groups in which the derived groups of all 2-generator subgroups are cyclic”

Groups with many nilpotent subgroups

Patrizia Longobardi, Mercede Maj, Avinoam Mann, Akbar Rhemtulla (1996)

Rendiconti del Seminario Matematico della Università di Padova

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The divisible radical of a group

B.A.F. Wehrfritz (2009)

Open Mathematics

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We consider the existence or otherwise of canonical divisible normal subgroups of groups in general. We present more counterexamples than positive results. These counterexamples constitute the substantive part of this paper.

The nilpotency of some groups with all subgroups subnormal.

Leonid A. Kurdachenko, Howard Smith (1998)

Publicacions Matemàtiques

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Let G be a group with all subgroups subnormal. A normal subgroup N of G is said to be G-minimax if it has a finite G-invariant series whose factors are abelian and satisfy either max-G or min- G. It is proved that if the normal closure of every element of G is G-minimax then G is nilpotent and the normal closure of every element is minimax. Further results of this type are also obtained.