A representation of the prolongations of a G−structure

‎In this paper‎, ‎we describe the general group of order two‎ $GP^2_n$‎. ‎Then‎, ‎we prove an arbitrary prolongation of a Lie subgroup‎ ‎of $GL(n,‎\Re)$ is a direct sum of additive Lie group of the form‎ ‎$\Re^{\tilde{n}}$ and a Lie subgroup of $GL(n,‎\Re)$‎. ‎Then we prove‎ ‎that an arbitrary prolongation of a Lie subalgebra of $Mat(n \times n)$ is‎ ‎a direct sum of an additive Lie subalgebra of the form $\Re^{\tilde{n}}$‎ ‎and a Lie subalgebra of $Mat(n\times n)$‎. ‎In conclusion structure group‎ ‎of every k'th order Geometric structure on a given $n-$dimmentinal manifold‎ ‎is isomorphic to an additive standard group $\Re^{\tilde{n}}$‎, ‎with‎ ‎$0\leq\tilde{n}\leq k\times\frac{n^2(3n-1)}{2}$‎, ‎and a Lie subgroup‎ ‎of $GL(n‎,‎\Re)$‎.