Suborbit Structure of Permutation $p$-Groups and an Application to Cayley Digraph Isomorphism
Printed: Jun 2004
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.
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.)