  We prove that if the group of isometries of C(X,E) is algebraically
reflexive, then the group of n-isometries is also algebraically reflexive.
Here, X is a compact Hausdorff space and E is a Banach space. As a corollary to
this, we establish the algebraic reflexivity of the set of generalized
bi-circular projections on C(X,E).
