John Bamberg and Cheryl E. Praeger

A finite permutation group is said to be innately transitive if it contains a transitive minimal normal subgroup. In this paper, we give a characterisation and structure theorem for the finite innately transitive groups, as well as describing those innately transitive groups which preserve a product decomposition. The class of innately transitive groups contains all primitive and quasiprimitive groups.

2000 Mathematical Subject Classification: 20B05, 20B15.

E-mail:
john.bam@maths.uwa.edu.au
praeger@maths.uwa.edu.au