On the Isomorphism Problem of {\bf p}-Endomorphisms

This thesis extends the Hoffman-Rudolph tvwB criterion defined for uniformly p-to-1 endomorphisms to show that it still gives a sufficient condition for a given $\mathbf{p}$-endomorphism to be one-sided Bernoulli. We also prove that given any two tvwB group extensions of the one-sided $\mathbf{p}$-shift, we can find an isomorphism preserving the natrual $\mathbb{N}\times G$-actions.