Minimal non-solvable Bieberbach groups

Rafa{\l} Lutowski; Andrzej Szczepa\'nski

arXiv:2302.11368·math.GR·February 24, 2023·Exp. Math.

Minimal non-solvable Bieberbach groups

Rafa{\l} Lutowski, Andrzej Szczepa\'nski

PDF

Open Access

TL;DR

This paper proves that the smallest dimension for non-solvable Bieberbach groups is 15, establishing a minimal boundary for such groups.

Contribution

It demonstrates that the minimal dimension for non-solvable Bieberbach groups is exactly 15, clarifying a key structural property of these groups.

Findings

01

Non-solvable Bieberbach groups exist in dimension 15

02

Dimension 15 is minimal for such groups

03

Provides a definitive lower bound for non-solvable Bieberbach groups

Abstract

It has been shown by several authors that there exists a non-solvable Bieberbach group of dimension $15$ . In this note we show that this is in fact a minimal dimension for such kind of 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

TopicsRings, Modules, and Algebras · Finite Group Theory Research · Advanced Topology and Set Theory