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

Published:2004-06-01
Printed: Jun 2004
• Brian Alspach
• Shaofei Du
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## Abstract

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.
 MSC Classifications: 20B25 - Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX] 05C60 - Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)

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