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. We also establish several new relations between singly-generated
closed classes.Comment: 22 page

Flores, Ramón

Rodríguez, José L.

English

arXiv

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

Flores Díaz, Ramón Jesús

idUS. Depósito de Investigación Universidad de Sevilla

Generators and closed classes of groups

The first author was partially supported by FEDER-MEC grants MTM2010-20692 and MTM-2016-76453-C2-1-P. Second-named author was supported by grant MTM2016-76453-C2-2-P and grant FQM-213 of the Junta de Andalucía.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

Generators and closed classes of groups

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