On Joinability by Horizontal Broken Lines on the Engel Group

On Joinability by Horizontal Broken Lines on the Engel Group Full article

Journal

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Output data

Year: 2026, Volume: 64, Number: 1, DOI: 10.1007/s10469-026-09807-7

Tags

horizontal curve, broken line, Engel group

Authors

Greshnov A.V. ^1,3 , Tryamkin M.V. ²

Affiliations

1	Novosibirsk State University and Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
2	Russian Technological University MIREA, Moscow, Russia
3	Novosibirsk State University

Funding (1)

Министерство науки и высшего образования РФ

075-15-2025-349

We prove that almost all points of the Engel group Eα,β are joined with its neutral element by basis horizontal k-broken lines LE k, k 4, the links of which are segments of integral lines of basis horizontal left-invariant vector fields X, Y of the Lie algebra of the group Eα,β. Furthermore, there exist elements of the group Eα,β that cannot be joined by basis horizontal k-broken lines LE k, k 4. We prove that all points of the Engel group Eα,β are joined with its neutral element by basis horizontal k-broken lines LE k, k 6.

Greshnov A.V. , Tryamkin M.V.
On Joinability by Horizontal Broken Lines on the Engel Group
Algebra and Logic. 2026. V.64. N1. DOI: 10.1007/s10469-026-09807-7 WOS Scopus OpenAlex

Submitted:	Oct 14, 2024
Accepted:	Jun 4, 2025
Published online:	Jan 26, 2026

Web of science:	WOS:001669099200001
Scopus:	2-s2.0-105028777529
OpenAlex:	W7125675767

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