TY - JOUR

T1 - On Joinability by Horizontal Broken Lines on the Engel Group

AU - Greshnov, A. V.

AU - Tryamkin, M. V.

N1 - Greshnov, A.V., Tryamkin, M.V. On Joinability by Horizontal Broken Lines on the Engel Group. Algebra Logic (2026). https://doi.org/10.1007/s10469-026-09807-7 This work was supported by the Mathematical Center in Akademgorodok, under Agreement with the Ministry of Science and Higher Education of the Russian Federation (Agreement No. 075-15-2025-349 dated April 29, 2025).

PY - 2026/1/26

Y1 - 2026/1/26

N2 - We prove that almost all points of the Engel group Eα,β are joined with its neutral element by basis horizontal k-broken lines Lkε,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 Lkε,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 Lkε,k≤6.

AB - We prove that almost all points of the Engel group Eα,β are joined with its neutral element by basis horizontal k-broken lines Lkε,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 Lkε,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 Lkε,k≤6.

KW - Engel group

KW - broken line

KW - horizontal curve

UR - https://www.scopus.com/pages/publications/105028777529

UR - https://www.mendeley.com/catalogue/39f3f4f5-3d1c-36ca-b5ec-6b9695438b94/

U2 - 10.1007/s10469-026-09807-7

DO - 10.1007/s10469-026-09807-7

M3 - Article

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

ER -