Isometry groups of $k$-curvature homogeneous pseudo-Riemannian manifolds

summary:In 2005 Gilkey and Nik\v cevi\'c introduced complete $(p+2)$-curvature homogeneous pseudo-Rie\-mannian manifolds of neutral signature $(3 + 2p, 3 + 2p)$, which are $0$-modeled on an indecomposable symmetric space, but which are not $(p + 3)$-curvature homogeneous. In this paper the authors continue their study of the same family of manifolds by examining their isometry groups and the isometry groups of their $k$-models