Disjoint direct product decompositions of permutation groups. (January 2022)

• Record Type: Journal Article
• Authors: Chang, Mun See; Jefferson, Christopher
• Is Part Of: Journal of symbolic computation. Volume 108(2022)
• Page Start: 1
• Page End: 16
• Publication Date: 2022-01
• Subjects: Permutation group -- Computation -- Direct product -- Subdirect product -- Decomposition -- Computer algebra system; 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.2021.04.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Let H ≤ S n be an intransitive group with orbits Ω 1, Ω 2, …, Ω k . Then certainly H is a subdirect product of the direct product of its projections onto each orbit, H | Ω 1 × H | Ω 2 × … × H | Ω k . Here we provide a polynomial time algorithm for computing the finest partition P of the H -orbits such that H = ∏ c ∈ P H | c and we demonstrate its usefulness in some applications.