Generators and closed classes of groups

• Autores: Ramón Jesús Flores Díaz , José Luis Rodríguez Blancas
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 65, Nº 2, 2021, págs. 431-457
• Idioma: inglés
• DOI: 10.5565/publmat6522102
• Enlaces
  • Texto completo
• Resumen

  • We show that, in the category of groups, every singly-generated class which is closed under isomorphisms, direct limits, and extensions is also singly-generated under isomorphisms and direct limits, and in particular is co-reflective. In this way, we extend to the group-theoretic framework the topological analogue proved by Chach´olski, Parent, and Stanley in 2004. We also establish several new relations between singly-generated closed classes.

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