Classification of gauge groups in terms of algebraic structure of first class constraints

Properties of gauge transformations for singular Lagrangians are investigated to classify types of gauge groups. A general method of the classification is proposed based on properties of structure functions of the Poisson brackets (or the commutators) of first class constraints. A remarkable result is that the algebraic structure of the gauge group is essentially determined by the first class constraints of the final step of constraint series which are required successively from the stationarity conditions of the constraints. Owing to this consequence, the classification of gauge groups is made simple and transparent. The structure and property of the gauge group can be characterized in terms of the algebraic structure functions among the final step constraints and the number of the steps of the constraints series. The formulation proposed will give a clue to find new types of gauge groups.