J. Aust. Math. Soc.  80 (2006), 45-63
Seminormal and subnormal subgroup lattices for transitive permutation groups

 Cheryl E. Praeger   School of Mathematics and Statistics   The University of Western Australia   35 Stirling Highway   Crawley WA 6009   Australia  praeger@maths.uwa.edu.au

Abstract
Various lattices of subgroups of a finite transitive permutation group G can be used to define a set of `basic' permutation groups associated with G that are analogues of composition factors for abstract finite groups. In particular, G can be embedded in an iterated wreath product of a chain of its associated basic permutation groups. The basic permutation groups corresponding to the lattice of all subgroups of G containing a given point stabiliser are a set of primitive permutation groups. We introduce two new subgroup lattices contained in , called the seminormal subgroup lattice and the subnormal subgroup lattice. For these lattices the basic permutation groups are quasiprimitive and innately transitive groups, respectively.