On profinite groups with commutators covered by nilpotent subgroups

• Pavel Shumyatsky ^[1]
  1. [1] Universidade de Brasília

     Universidade de Brasília

     Brasil

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 4, 2016, págs. 1331-1339
• Idioma: inglés
• DOI: 10.4171/RMI/919
• Texto completo no disponible (Saber más ...)
• Resumen

  • The following results about a profinite group G are obtained. The commutator subgroup G′ is finite if and only if G´ is covered by countably many abelian subgroups. The group G is finite-by-nilpotent if and only if G is covered by countably many nilpotent subgroups. The main result is that the commutator subgroup G′ is finite-by-nilpotent if and only if the set of all commutators in G is covered by countably many nilpotent subgroups.