Krull dimension of solvable groups
A. Myasnikov, N. Romanovskiy
TL;DR
This paper proves that free solvable groups and a broader class called rigid groups have finite Krull dimension, by analyzing the algebraic structure of limit solvable groups, including fully residually free solvable groups.
Contribution
It establishes the finite Krull dimension for free solvable and rigid groups, expanding understanding of their algebraic properties.
Findings
Free solvable groups have finite Krull dimension.
The class of rigid groups also has finite Krull dimension.
Analysis of limit solvable groups reveals their algebraic structure.
Abstract
In this paper we prove that free solvable groups have finite Krull dimension. In fact, this is true for much wider class of solvable groups, termed rigid groups. Along the way we study the algebraic structure of the limit solvable groups (fully residually free solvable groups).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory