The use of permutation representations in structural computations in large finite matrix groups. (November 2019)

• Record Type: Journal Article
• Authors: Cannon, John J.; Holt, Derek F.; Unger, William R.
• Is Part Of: Journal of symbolic computation. Volume 95(2019)
• Page Start: 26
• Page End: 38
• Publication Date: 2019-11
• Subjects: Permutation representation -- Finite matrix group -- Structural computation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.09.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We determine the minimal degree permutation representations of all finite groups with trivial soluble radical, and describe applications to structural computations in large finite matrix groups that use the output of the CompositionTree algorithm. We also describe how this output can be used to help find an effective base and strong generating set for such groups. We have implemented the resulting algorithms in Magma, and we report on their performance.