Generators and closed classes of groups
Ram\'on Flores, Jos\'e L. Rodr\'iguez
TL;DR
This paper investigates the structure of certain classes of groups, showing that singly-generated classes closed under key operations are also co-reflective, and explores new relationships between these classes.
Contribution
It proves that singly-generated closed classes of groups are also singly-generated under isomorphisms and direct limits, and establishes new relations among these classes.
Findings
Singly-generated closed classes are co-reflective.
Such classes are also singly-generated under isomorphisms and direct limits.
New relations between singly-generated closed classes are established.
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. We also establish several new relations between singly-generated closed classes.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras · Fuzzy and Soft Set Theory