Abstract
The velocity structure functions of fully developed turbulence are studied by only using homogeneity, isotropy, scale invariance and single scale dependence of variables. Scale covariant laws showing intermittency are derived. The regular laws yield a finite bound of the scaling exponents of positive moments. In the moment space, they induce an invariance of scaling exponents by moment translation which generalizes the "hidden symmetry" postulated by She and Lévêque for the moments of a nondimensional rate of energy dissipation.