Using canonical methods, we study the invariance properties of a bosonic p-brane propagating in a curved background locally diffeomorphic to MG, where M is space-time and G a group manifold. The action is that of a gauged sigma model in p+1 dimensions coupled to a Yang-Mills field and a (p+1) form in M. We construct the generators of Yang-Mills and tensor gauge transformations and exhibit the role of the (p+1) form in canceling the potential Schwinger terms. We also discuss the Noether currents associated with the global symmetries of the action and the question of the existence of infinite-dimensional symmetry algebras, analogous to the Kac-Moody symmetry of the string.
