Bounding the composition length of primitive permutation groups and completely reducible linear groups
Group Theory
2018-03-15 v2
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.
Cite
@article{arxiv.1712.05520,
title = {Bounding the composition length of primitive permutation groups and completely reducible linear groups},
author = {S. P. Glasby and Cheryl E. Praeger and Kyle Rosa and Gabriel Verret},
journal= {arXiv preprint arXiv:1712.05520},
year = {2018}
}
Comments
23 pages; a few minor corrections following the referee's comments