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 anddirect limits, and in particular is co-reflective. In this way, we extend to the group-theoretic frameworkthe topological analogue proved by Chachólski, Parent, and Stanley in 2004. We also establish several new relations between singly-generated closed classes.
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.
"Generators and closed classes of groups." Publ. Mat. 65 (2) 431 - 457, 2021. https://doi.org/10.5565/PUBLMAT6522102