Abstract
It is shown that the usual association of a conservation law to a continuous symmetry group given by Noether's theorem is only correct when the group can be defined by means of a finite number of parameters. This is the case, for instance, of the inhomogeneous proper Lorentz group and of the phase groups. The meaning of Noether's theorem for those groups, like the gauge groups, that cannot be expressed with a finite number of parameters, is discussed in detail. In addition to the well-known gauge transformations of the first and second kind, more general gauge groups of the Yang-Mills type are also considered.
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