MSI Colloquium

4pm Friday 16 April 2004

Cheryl Praeger
University of Western Australia

Subgroup lattices and group actions

Various lattices of subgroups of a finite transitive permutation group G can be used to define sets of `basic' permutation groups associated with G that are analogues of the composition factors for an abstract finite group. In particular G can be embedded in an iterated wreath product of a chain of its associated basic permutation groups. I will illustrate how this works, and introduce three types of lattices that correspond to three different types of basic groups, one family of which are the primitive groups. I will discuss several applications where the different types of basic groups arise naturally in combinatorics.




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