On the Engel group we solve the problem of finding the minimal number of segments of integral lines of left-invariant basis horizontal vector fields necessary for joining an arbitrary pair of points. We prove the best version of Rashevskii–Chow Theorem on Engel group.
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Alexander Greshnov, Optimal horizontal joinability on the Engel group. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 3, pp. 535–547DOI 10.4171/RLM/947