98-11E

A tangent Lie group with elements and group operations which are (jet) prolongations of those corresponding to another Lie group is examined. An action of such extended Lie group on differentiable manifold and its tangent bundle is defined by using contact transformations. It turned out that a tangent Lie symmetrical Lagrangian describes the dynamical system with first-class constraints. The infinitesimal symmetries originated from a tangent Lie group of symmetries are investigated.