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# Suborbit Structure of Permutation $p$-Groups and an Application to Cayley Digraph Isomorphism

Let $P$ be a transitive permutation group of order $p^m$, $p$ an odd prime, containing a regular cyclic subgroup. The main result of this paper is a determination of the suborbits of $P$. The main result is used to give a simple proof of a recent result by J.~Morris on Cayley digraph isomorphisms.