  Using canonical methods, we study the invariance properties of a bosonic
$p$--brane propagating in a curved background locally diffeomorphic to $M\times
G$, where $M$ is spacetime 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 cancelling
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.
