  A microsymmetry group \(G_{p}\), at \(p \in M\), of a metric structure, is a set of invertible, linear maps of the tangent space \(T(M_{p})\) onto itself, which preserve the infinitesimal distance function at \(p \in M\). For every \(p \in M, G_{p}\) is isomorphic to one and the same abstract group. 