Abnormal Geodesics for a Carnot Group with Growth Vector $(2, 3, 5, 8, 14)$

This paper is concerned with abnormal geodesics on the Carnot group with growth vector $(2, 3, 5, 8, 14)$. Because of a large number of symmetries, this problem reduces to an analysis of the five-dimensional flow. Using the Kovalevskaya method, integrable cases of the resulting system are identified. For these cases, first integrals and explicit solutions are found. It is shown that in the general case the system admits no additional meromorphic first integrals. The paper concludes by discussing some problems regarding the abnormal geodesics on Lie groups.