Transitive permutation groups of primesquared degree
Abstract
We explicitly determine all of the transitive groups of degree psquared, p a prime, whose Sylow psubgroup is not the wreath product of two cyclic groups of order p. Furthermore, we provide a general description of the transitive groups of degree psquared whose Sylow psubgroup 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 psquared, explicitly determine the full automorphism group of Cayley graphs of abelian groups of order psquared, and find all nonnormal Cayley graphs of order psquared.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2000
 arXiv:
 arXiv:math/0012192
 Bibcode:
 2000math.....12192D
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Combinatorics;
 20B35;
 05C25;
 05E20
 EPrint:
 29 pages, no figures. This version corrects an error in the statement of Theorem 12