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2021 Generators and closed classes of groups
Ramón Flores, José L. Rodríguez
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Publ. Mat. 65(2): 431-457 (2021). DOI: 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 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.

Funding Statement

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.

Citation

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Ramón Flores. José L. Rodríguez. "Generators and closed classes of groups." Publ. Mat. 65 (2) 431 - 457, 2021. https://doi.org/10.5565/PUBLMAT6522102

Information

Received: 30 September 2019; Revised: 2 October 2020; Published: 2021
First available in Project Euclid: 21 June 2021

Digital Object Identifier: 10.5565/PUBLMAT6522102

Subjects:
Primary: 20E34
Secondary: 20E22, 55P60

Rights: Copyright © 2021 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.65 • No. 2 • 2021
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