Transitive Permutation Groups of Prime-Squared Degree

By Edward Dobson, Dave Witte. 2000

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AbstractWe explicitly determine all of the transitive groups of degree p2, p a prime, whose Sylow p-subgroup is not isomorphic to the wreath product $$\mathbb{Z}_p \wr \mathbb{Z}_p$$ . Furthermore, we provide a general description of the transitive groups of degree p2 whose Sylow p-subgroup is isomorphic to $$\mathbb{Z}_p \wr \mathbb{Z}_p$$ , and explicitly determine most of them. As applications, we solve the Cayley Isomorphism problem for Cayley objects of an abelian group of order p2, explicitly determine the full automorphism group of Cayley graphs of abelian groups of order p2, and find all nonnormal Cayley graphs of order p2.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/56b2b787876137c274ffcbc300f688b2be289475