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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.
|Number of pages||16|
|Journal||Journal of the London Mathematical Society|
|Publication status||Published - 1 Dec 2018|
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Permutation groups: factorisations, structure and applications
1/01/16 → 2/02/19