Minimal and random generation of permutation and matrix groups
Holt, Derek F. and Roney-Dougal, Colva M.. (2013) Minimal and random generation of permutation and matrix groups. Journal of Algebra, Volume 387 (Number ). pp. 195-214. ISSN 0021-8693Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.jalgebra.2013.03.035
We prove explicit bounds on the numbers of elements needed to generate various types of finite permutation groups and finite completely reducible matrix groups, and present examples to show that they are sharp in all cases. The bounds are linear in the degree of the permutation or matrix group in general, and logarithmic when the group is primitive. They can be combined with results of Lubotzky to produce explicit bounds on the number of random elements required to generate these groups with a specified probability. These results have important applications to computational group theory. Our proofs are inductive and largely theoretical, but we use computer calculations to establish the bounds in a number of specific small cases.
|Item Type:||Journal Article|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Journal of Algebra|
|Page Range:||pp. 195-214|
|Access rights to Published version:||Restricted or Subscription Access|
Actions (login required)