Generators and closed classes of groups
- 1 July 2021
- journal article
- research article
- Published by Universitat Autonoma de Barcelona in Publicacions Matemàtiques
- Vol. 65 (2), 431-457
- https://doi.org/10.5565/publmat6522102
Abstract
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 Chacholski, Parent, and Stanley in 2004. We also establish several new relations between singly-generated closed classes.Keywords
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