Disjoint direct product decompositions of permutation groups
Abstract
Let H ≤ Sn be an intransitive group with orbits Ω1, Ω2, ... , Ωk. Then certainly H is a subdirect product of the direct product of its projections on each orbit, H|Ω1 x H|Ω2 x ... x H|Ωk. Here we provide a polynomial time algorithm for computing the finest partition P of the H-orbits such that H = Πc∈P H|c and we demonstrate its usefulness in some applications.
Citation
Chang , M S & Jefferson , C A 2022 , ' Disjoint direct product decompositions of permutation groups ' , Journal of Symbolic Computation , vol. 108 , pp. 1-16 . https://doi.org/10.1016/j.jsc.2021.04.003
Publication
Journal of Symbolic Computation
Status
Peer reviewed
ISSN
0747-7171Type
Journal article
Rights
Copyright © 2021 Elsevier Ltd. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jsc.2021.04.003.
Description
Funding: The first author is supported by an Engineering and Physical Sciences Research Council grant (EP/P015638/1). The second author is supported by a Royal Society University Research Fellowship (URF\R\180015).Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.