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In this brief article an internal symmetry of a generic metric compatiblespace-time connection, metric and generalized volume element is introduced. Thesymmetry arises naturally by considering a space-time connection containing ageneric torsion tensor, and would otherwise be missed in the absence oftorsion. When the transformation is applied to the Hilbert-Einstein action itis shown that by a choice of gauge all possible field theories arising from theHilbert-Einstein action are equivalent to the standard theory of gravitydescribed by general relativity.

Internal Symmetry of Space-Time Connections with Torsion