Title: Bounding the composition length of primitive permutation groups and completely reducible linear groups,
Abstract: We obtain upper bounds on the composition length of a finite permutation
group in terms of the degree and the number of orbits, and analogous bounds for
primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper
bounds on the composition length of a finite completely reducible linear group
in terms of some of its parameters. In almost all cases we show that the bounds
are sharp, and describe the extremal examples.