Disjoint direct product decompositions of permutation groups. (January 2022) - Chang, Mun See; Jefferson, Christopher
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.