Abstract
The theory of equations of the Dirac type which are form-invariant under general finite continuous groups of point transformations in space-time is developed. The possible equations invariant under a given group depend on the structure of the group, but in each case the required invariance imposes a set of linear homogeneous relations on the $\ensuremath{\beta}$-operators with which any assumed algebra must be consistent. It is shown that the algebra appropriate to the general equation possessing form-invariance under the inhomogeneous Lorentz group is necessarily of infinite order.
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