Transitive permutation groups of prime-squared degree

Details Transitive permutation groups of prime-squared degree Transitive permutation groups of prime-squared degree

2000-12-19

arxiv.org/abs/math/0012192v2

Journal of Algebraic Combinatorics 16 (2002) 43-69

Mathematics

Group Theory

29 pages, no figures. This version corrects an error in the statement of Theorem 12

Scientific paper

We explicitly determine all of the transitive groups of degree p-squared, p a prime, whose Sylow p-subgroup is not the wreath product of two cyclic groups of order p. Furthermore, we provide a general description of the transitive groups of degree p-squared whose Sylow p-subgroup is such a wreath product, and explicitly determine most of them. As applications, we solve the Cayley Isomorphism problem for Cayley objects of an abelian group of order p-squared, explicitly determine the full automorphism group of Cayley graphs of abelian groups of order p-squared, and find all nonnormal Cayley graphs of order p-squared.

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