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Home > Vol 16, No 1 (2002)

Edward Dobson¹ and Dave Witte²

¹Mississippi State University Department of Mathematics and Statistics Mississippi State MS 39762 USA
²Oklahoma State University Department of Mathematics Stillwater OK 74078 USA

We explicitly determine all of the transitive groups of degree p ², p a prime, whose Sylow p-subgroup is not isomorphic to the wreath product \mathbb Z _p \wr \mathbb Z _p \mathbb{Z}_p \wr \mathbb{Z}_p . Furthermore, we provide a general description of the transitive groups of degree p ² whose Sylow p-subgroup is isomorphic to \mathbb Z _p \wr \mathbb Z _p \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 p ², explicitly determine the full automorphism group of Cayley graphs of abelian groups of order p ², and find all nonnormal Cayley graphs of order p ².

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