Residually rationally solvable one-relator groups
Marco Linton

TL;DR
This paper investigates the structure of one-relator groups, showing their rational derived series has specific properties and providing a precise characterization of when such groups are residually rationally solvable.
Contribution
It introduces a detailed analysis of the rational derived series in one-relator groups and characterizes residual rational solvability.
Findings
The intersection of the rational derived series is rationally perfect.
This intersection is normally generated by a single element.
Provides a precise criterion for residual rational solvability.
Abstract
We show that the intersection of the rational derived series of a one-relator group is rationally perfect and is normally generated by a single element. As a corollary, we characterise precisely when a one-relator group is residually rationally solvable.
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Taxonomy
TopicsGeometric and Algebraic Topology · Finite Group Theory Research
