Abstract
This paper studies the canonical symmetric connection del associated to any Lie group G. The salient properties of del are stated and proved. The Lie symmetries of the geodesic system of a general linear connection are formulated. The results are then applied to del in the special case where the Lie algebra g of G, has a codimension one abelian nilradical. The conditions that determine a Lie symmetry in such a case are completely integrated. Finally the results obtained are compared with some four-dimensional Lie groups whose Lie algebras have three-dimensional abelian nilradicals, for which the calculations were performed by MAPLE. (C) 2021 The Authors. Published by Atlantis Press B.V.