In this paper we study finite non abelian solvable groups in which every proper normal subgroup is abelian, and non-solvable ones in which every proper normal subgroup is abelian and has a basis of at most two elements.
In this paper we study finite non abelian solvable groups in which every proper normal subgroup is abelian, and non-solvable ones in which every proper normal subgroup is abelian and has a basis of at most two elements.
In questa nota si studiano i gruppi finiti non supersolubili che hanno un solo sottogruppo normale massimale, e per cui ogni sottogruppo normale proprio e ogni immagine epimorfica propria è supersolubile.
In this paper we study finite non abelian groups in which every proper normal subgroup and every proper epimorphic image is abelian. Also we study finite non nilpotent groups in which every normal subgroup and every proper epimorphic image is nilpotent and those finite soluble non nilpotent groups in which every proper normal subgroup is nilpotent.
In this paper we study finite non abelian groups in which every proper normal subgroup and every proper epimorphic image is abelian. Also we study finite non nilpotent groups in which every normal subgroup and every proper epimorphic image is nilpotent and those finite soluble non nilpotent groups in which every proper normal subgroup is nilpotent.
We obtain an algebraic interpretation by means of the Picard-Vessiot theory of a result by Ziglin about the self-intersection of complex separatrices of time-periodically perturbed one-degree of freedom complex analytical Hamiltonian systems.
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