The nilpotency of some groups with all subgroups subnormal

• Autores: Howard Smith, Leonid A. Kurdachenko
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 42, Nº 2, 1998, págs. 411-421
• Idioma: inglés
• DOI: 10.5565/publmat_42298_08
• Títulos paralelos:
  • Nilpotencia de algunos grupos con todos sus subgrupos subnormales
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• Resumen

  • 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.