Displaying similar documents to “Amalgams of torsion-free nilpotent groups of class three”

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.

On hypercentral groups

B. Wehrfritz (2007)

Open Mathematics

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Let G be a hypercentral group. Our main result here is that if G/G’ is divisible by finite then G itself is divisible by finite. This extends a recent result of Heng, Duan and Chen [2], who prove in a slightly weaker form the special case where G is also a p-group. If G is torsion-free, then G is actually divisible.

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 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.