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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Patrizia Longobardi, Mercede Maj, Avinoam Mann, Akbar Rhemtulla (1996)
Rendiconti del Seminario Matematico della Università di Padova
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John C. Lennox, Derek J. S. Robinson (1980)
Rendiconti del Seminario Matematico della Università di Padova
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Hilton, Peter, Militello, Robert (1996)
International Journal of Mathematics and Mathematical Sciences
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Jutta Hausen (1981)
Rendiconti del Seminario Matematico della Università di Padova
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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.
Ali Boukaroura (2004)
Rendiconti del Seminario Matematico della Università di Padova
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Tarek Rouabhi, Nadir Trabelsi (2007)
Rendiconti del Seminario Matematico della Università di Padova
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Berthold J. Maier (1984)
Rendiconti del Seminario Matematico della Università di Padova
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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.